Timmermann, T.; Van Daele, A.; Wang, S. H. Pairing and duality of algebraic quantum groupoids. (English) Zbl 1505.16046 Int. J. Math. 33, No. 7, Article ID 2250055, 50 p. (2022). Reviewer: Arkadiusz Bochniak (Garching) MSC: 16T05 16K40 PDFBibTeX XMLCite \textit{T. Timmermann} et al., Int. J. Math. 33, No. 7, Article ID 2250055, 50 p. (2022; Zbl 1505.16046) Full Text: DOI arXiv
Landstad, Magnus B.; Van Daele, Alfons Finite quantum hypergroups. arXiv:2209.13282 Preprint, arXiv:2209.13282 [math.QA] (2022). MSC: 20N20 16T05 46L67 BibTeX Cite \textit{M. B. Landstad} and \textit{A. Van Daele}, ``Finite quantum hypergroups'', Preprint, arXiv:2209.13282 [math.QA] (2022) Full Text: arXiv OA License
van Daele, Alfons From Hopf algebras to topological quantum groups. A short history, various aspects and some problems. (English) Zbl 1467.16034 Dąbrowski, Ludwik (ed.) et al., Quantum dynamics. Dedicated to Professor Paul Baum. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Cent. Publ. 120, 179-220 (2020). MSC: 16T05 16-06 46-06 46L67 22D25 PDFBibTeX XMLCite \textit{A. van Daele}, Banach Cent. Publ. 120, 179--220 (2020; Zbl 1467.16034) Full Text: DOI arXiv
Kahng, Byung-Jay; Van Daele, Alfons A class of \(C^\ast\)-algebraic locally compact quantum groupoids. II: Main theory. (English) Zbl 1436.46054 Adv. Math. 354, Article ID 106761, 85 p. (2019). MSC: 46L67 46L51 81R50 16T05 22A22 PDFBibTeX XMLCite \textit{B.-J. Kahng} and \textit{A. Van Daele}, Adv. Math. 354, Article ID 106761, 85 p. (2019; Zbl 1436.46054) Full Text: DOI arXiv
Kahng, Byung-Jay; Van Daele, Alfons Separability idempotents in \(C^{\ast}\)-algebras. (English) Zbl 1412.46083 J. Noncommut. Geom. 12, No. 3, 997-1040 (2018). MSC: 46L89 46L51 16T05 22A22 PDFBibTeX XMLCite \textit{B.-J. Kahng} and \textit{A. Van Daele}, J. Noncommut. Geom. 12, No. 3, 997--1040 (2018; Zbl 1412.46083) Full Text: DOI arXiv
Timmermann, Thomas; Van Daele, Alfons Multiplier Hopf algebroids: basic theory and examples. (English) Zbl 1440.16035 Commun. Algebra 46, No. 5, 1926-1958 (2018). MSC: 16T05 PDFBibTeX XMLCite \textit{T. Timmermann} and \textit{A. Van Daele}, Commun. Algebra 46, No. 5, 1926--1958 (2018; Zbl 1440.16035) Full Text: DOI arXiv
Kahng, Byung-Jay; van Daele, Alfons A class of \(C^\ast\)-algebraic locally compact quantum groupoids. I: Motivation and definition. (English) Zbl 1397.46055 Int. J. Math. 29, No. 4, Article ID 1850029, 33 p. (2018). MSC: 46L65 46L51 81R50 16T05 22A22 PDFBibTeX XMLCite \textit{B.-J. Kahng} and \textit{A. van Daele}, Int. J. Math. 29, No. 4, Article ID 1850029, 33 p. (2018; Zbl 1397.46055) Full Text: DOI arXiv
Van Daele, Alfons Algebraic quantum groupoids - An example. arXiv:1702.04903 Preprint, arXiv:1702.04903 [math.RA] (2017). MSC: 16Txx BibTeX Cite \textit{A. Van Daele}, ``Algebraic quantum groupoids - An example'', Preprint, arXiv:1702.04903 [math.RA] (2017) Full Text: arXiv OA License
Van Daele, Alfons; Wang, Shuanhong Weak multiplier Hopf algebras III. Integrals and duality. arXiv:1701.04951 Preprint, arXiv:1701.04951 [math.RA] (2017). MSC: 16Txx BibTeX Cite \textit{A. Van Daele} and \textit{S. Wang}, ``Weak multiplier Hopf algebras III. Integrals and duality'', Preprint, arXiv:1701.04951 [math.RA] (2017) Full Text: arXiv OA License
Timmermann, Thomas; Van Daele, Alfons Multiplier Hopf algebroids arising from weak multiplier Hopf algebras. (English) Zbl 1343.16027 Ciccoli, Nicola (ed.) et al., From Poisson brackets to universal quantum symmetries. Selected papers of the workshop, IMPAN, Warsaw, August 18–22, 2014. Warsaw: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-29-4/pbk). Banach Center Publications 106, 73-110 (2015). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 16T05 PDFBibTeX XMLCite \textit{T. Timmermann} and \textit{A. Van Daele}, Banach Cent. Publ. 106, 73--110 (2015; Zbl 1343.16027) Full Text: DOI arXiv
Van Daele, Alfons Locally compact quantum groups. A von Neumann algebra approach. (English) Zbl 1312.46055 SIGMA, Symmetry Integrability Geom. Methods Appl. 10, Paper 082, 41 p. (2014). MSC: 46L10 43A99 17B37 16T20 PDFBibTeX XMLCite \textit{A. Van Daele}, SIGMA, Symmetry Integrability Geom. Methods Appl. 10, Paper 082, 41 p. (2014; Zbl 1312.46055) Full Text: DOI arXiv EMIS
Delvaux, L.; Van Daele, A.; Wang, S. H. Bicrossproducts of algebraic quantum groups. (English) Zbl 1271.16032 Int. J. Math. 24, No. 1, Paper No. 1250131, 48 p. (2013). Reviewer: Loïc Foissy (Calais) MSC: 16T05 16T20 17B37 PDFBibTeX XMLCite \textit{L. Delvaux} et al., Int. J. Math. 24, No. 1, Paper No. 1250131, 48 p. (2013; Zbl 1271.16032) Full Text: DOI arXiv
Van Daele, Alfons; Wang, Shuanhong Weak multiplier Hopf algebras. Preliminaries, motivation and basic examples. (English) Zbl 1267.16030 Pusz, Wiesław (ed.) et al., Operator algebras and quantum groups. Proceedings of the conference, Warsaw, Poland, September 19–23, 2011. Warszawa: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-17-1/pbk). Banach Center Publications 98, 367-415 (2012). MSC: 16T05 16T20 17B37 46L89 PDFBibTeX XMLCite \textit{A. Van Daele} and \textit{S. Wang}, Banach Cent. Publ. 98, 367--415 (2012; Zbl 1267.16030) Full Text: DOI arXiv
Delvaux, L.; Van Daele, A.; Wang, Shuanhong A note on the antipode for algebraic quantum groups. (English) Zbl 1252.16028 Can. Math. Bull. 55, No. 2, 260-270 (2012). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 16T05 16T20 17B37 46L65 PDFBibTeX XMLCite \textit{L. Delvaux} et al., Can. Math. Bull. 55, No. 2, 260--270 (2012; Zbl 1252.16028) Full Text: DOI Link
Van Daele, A. Locally compact quantum groups. Radford’s \(S^4\) formula. (English) Zbl 1250.16026 Marcolli, Matilde (ed.) et al., Quantum groups and noncommutative spaces. Perspectives on quantum geometry. Based on the presentations at the workshop, Bonn, Germany, August 6–8, 2007. Wiesbaden: Vieweg+Teubner (ISBN 978-3-8348-1442-5/hbk; 978-3-8348-9831-9/ebook). Aspects of Mathematics E41, 130-145 (2011). MSC: 16T20 16T05 46L89 46L65 PDFBibTeX XMLCite \textit{A. Van Daele}, in: Quantum groups and noncommutative spaces. Perspectives on quantum geometry. Based on the presentations at the workshop, Bonn, Germany, August 6--8, 2007. Wiesbaden: Vieweg+Teubner. 130--145 (2011; Zbl 1250.16026) Full Text: DOI arXiv
Delvaux, L.; Van Daele, A. Algebraic quantum hypergroups. (English) Zbl 1206.43004 Adv. Math. 226, No. 2, 1134-1167 (2011). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 43A62 20G42 17B37 81R50 PDFBibTeX XMLCite \textit{L. Delvaux} and \textit{A. Van Daele}, Adv. Math. 226, No. 2, 1134--1167 (2011; Zbl 1206.43004) Full Text: DOI arXiv Link
De Commer, K.; Van Daele, A. Multiplier Hopf algebras imbedded in locally compact quantum groups. (English) Zbl 1226.16023 Rocky Mt. J. Math. 40, No. 4, 1149-1182 (2010). Reviewer: Adam Skalski (Warszawa) MSC: 16T05 46L65 46L89 17B37 22D35 43A22 16T20 PDFBibTeX XMLCite \textit{K. De Commer} and \textit{A. Van Daele}, Rocky Mt. J. Math. 40, No. 4, 1149--1182 (2010; Zbl 1226.16023) Full Text: DOI arXiv
Van Daele, A.; Wang, Shuanhong Pontryagin duality for bornological quantum hypergroups. (English) Zbl 1195.46075 Manuscr. Math. 131, No. 1-2, 247-263 (2010). MSC: 46L65 46A17 17B37 16T20 PDFBibTeX XMLCite \textit{A. Van Daele} and \textit{S. Wang}, Manuscr. Math. 131, No. 1--2, 247--263 (2010; Zbl 1195.46075) Full Text: DOI
Wang, S. H.; Van Daele, A.; Zhang, Y. H. Constructing quasitriangular multiplier Hopf algebras by twisted tensor coproducts. (English) Zbl 1186.16028 Commun. Algebra 37, No. 9, 3171-3199 (2009). Reviewer: Zhang Liangyun (Nanjing) MSC: 16T05 16S40 16T20 81R50 PDFBibTeX XMLCite \textit{S. H. Wang} et al., Commun. Algebra 37, No. 9, 3171--3199 (2009; Zbl 1186.16028) Full Text: DOI
Van Daele, A.; Wang, Shuanhong New braided crossed categories and Drinfel’d quantum double for weak Hopf group coalgebras. (English) Zbl 1154.16031 Commun. Algebra 36, No. 6, 2341-2386 (2008). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 16W30 18D10 57R56 PDFBibTeX XMLCite \textit{A. Van Daele} and \textit{S. Wang}, Commun. Algebra 36, No. 6, 2341--2386 (2008; Zbl 1154.16031) Full Text: DOI
Van Daele, Alfons; Wang, Shuanhong A class of multiplier Hopf algebras. (English) Zbl 1133.16029 Algebr. Represent. Theory 10, No. 5, 441-461 (2007). Reviewer: Sonia Natale (Cordoba) MSC: 16W30 17B37 PDFBibTeX XMLCite \textit{A. Van Daele} and \textit{S. Wang}, Algebr. Represent. Theory 10, No. 5, 441--461 (2007; Zbl 1133.16029) Full Text: DOI
Abd El-Hafez, A. T.; Delvaux, L.; Van Daele, A. Group-cograded multiplier Hopf (\(*\)-)algebras. (English) Zbl 1129.16027 Algebr. Represent. Theory 10, No. 1, 77-95 (2007). Reviewer: Li Fang (Hangzhou) MSC: 16W30 16W50 17B37 PDFBibTeX XMLCite \textit{A. T. Abd El-Hafez} et al., Algebr. Represent. Theory 10, No. 1, 77--95 (2007; Zbl 1129.16027) Full Text: DOI arXiv
Landstad, M. B.; Van Daele, A. Compact and discrete subgroups of algebraic quantum groups I. arXiv:math/0702458 Preprint, arXiv:math/0702458 [math.OA] (2007). MSC: 20N20 16W30 81R50 BibTeX Cite \textit{M. B. Landstad} and \textit{A. Van Daele}, ``Compact and discrete subgroups of algebraic quantum groups I'', Preprint, arXiv:math/0702458 [math.OA] (2007) Full Text: arXiv
Delvaux, L.; Van Daele, A. The Drinfel’d double versus the Heisenberg double for an algebraic quantum group. (English) Zbl 1056.16027 J. Pure Appl. Algebra 190, No. 1-3, 59-84 (2004). Reviewer: Sorin Dascalescu (Safat) MSC: 16W30 17B37 PDFBibTeX XMLCite \textit{L. Delvaux} and \textit{A. Van Daele}, J. Pure Appl. Algebra 190, No. 1--3, 59--84 (2004; Zbl 1056.16027) Full Text: DOI
Vaes, Stefaan; Van Daele, Alfons The Heisenberg commutation relations, commuting squares and the Haar measure on locally compact quantum groups. (English) Zbl 1247.46061 Combes, Jean-Michel (ed.) et al., Operator algebras and mathematical physics. Proceedings of the conference, Constanţa, Romania, July 2–7, 2001. Bucharest: Theta (ISBN 973-85432-2-3). 379-400 (2003). MSC: 46L65 16T20 22D99 43A80 81S05 PDFBibTeX XMLCite \textit{S. Vaes} and \textit{A. Van Daele}, in: Operator algebras and mathematical physics. Proceedings of the conference, Constanţa, Romania, July 2--7, 2001. Bucharest: Theta. 379--400 (2003; Zbl 1247.46061)
Van Daele, Alfons Multiplier Hopf\(^*\)-algebras with positive integrals: a laboratory for locally compact quantum groups. (English) Zbl 1176.22006 Vainerman, Leonid (ed.), Locally compact quantum groups and groupoids. Proceedings of the 69th meeting of theoretical physicists and mathematicians, Strasbourg, France, February 21–23, 2002. Berlin: Walter de Gruyter (ISBN 3-11-017690-4/pbk). IRMA Lect. Math. Theor. Phys. 2, 229-247 (2003). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 22D99 16T20 46L89 PDFBibTeX XMLCite \textit{A. Van Daele}, IRMA Lect. Math. Theor. Phys. 2, 229--247 (2003; Zbl 1176.22006) Full Text: arXiv
Vaes, Stefaan; Van Daele, Alfons Hopf \(C^*\)-algebras. (English) Zbl 1028.46100 Proc. Lond. Math. Soc., III. Ser. 82, No. 2, 337-384 (2001). Reviewer: Stefaan Vaes (Leuven) MSC: 46L65 46L07 46L89 PDFBibTeX XMLCite \textit{S. Vaes} and \textit{A. Van Daele}, Proc. Lond. Math. Soc. (3) 82, No. 2, 337--384 (2001; Zbl 1028.46100) Full Text: DOI arXiv
Drabant, Bernhard; Van Daele, Alfons Pairing and quantum double of multiplier Hopf algebras. (English) Zbl 0993.16024 Algebr. Represent. Theory 4, No. 2, 109-132 (2001). Reviewer: Sorin Dascalescu (Safat) MSC: 16W30 17B37 PDFBibTeX XMLCite \textit{B. Drabant} and \textit{A. Van Daele}, Algebr. Represent. Theory 4, No. 2, 109--132 (2001; Zbl 0993.16024) Full Text: DOI arXiv
Van Daele, Alfons Quantum groups with invariant integrals. (English) Zbl 0984.16038 Proc. Natl. Acad. Sci. USA 97, No. 2, 541-546 (2000). Reviewer: Sonia Natale (Cordoba) MSC: 16W30 16W35 81R50 17B37 PDFBibTeX XMLCite \textit{A. Van Daele}, Proc. Natl. Acad. Sci. USA 97, No. 2, 541--546 (2000; Zbl 0984.16038) Full Text: DOI
Kurose, Hideki; Van Daele, Alfons; Zhang, Yinhuo Corepresentation theory of multiplier Hopf algebras. II. (English) Zbl 1108.16302 Int. J. Math. 11, No. 2, 233-278 (2000). MSC: 16W30 PDFBibTeX XMLCite \textit{H. Kurose} et al., Int. J. Math. 11, No. 2, 233--278 (2000; Zbl 1108.16302) Full Text: DOI
Van Daele, Alfons; Zhang, Yinhuo The duality theorem for coactions of multiplier Hopf algebras. (English) Zbl 0978.16037 Van Oystaeyen, Freddy (ed.) et al., Interactions between ring theory and representations of algebras. Proceedings of the conference, Murcia, Spain. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 210, 413-422 (2000). Reviewer: Alan Koch (Decatur) MSC: 16W30 16S40 16W35 17B37 PDFBibTeX XMLCite \textit{A. Van Daele} and \textit{Y. Zhang}, Lect. Notes Pure Appl. Math. 210, 413--422 (2000; Zbl 0978.16037)
Van Daele, Alfons; Zhang, Yinhuo Corepresentation theory of multiplier Hopf algebras. I. (English) Zbl 0945.16033 Int. J. Math. 10, No. 4, 503-539 (1999). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 16W30 PDFBibTeX XMLCite \textit{A. Van Daele} and \textit{Y. Zhang}, Int. J. Math. 10, No. 4, 503--539 (1999; Zbl 0945.16033) Full Text: DOI
Drabant, Bernhard; Van Daele, Alfons; Zhang, Yinhuo Actions of multiplier Hopf algebras. (English) Zbl 0951.16013 Commun. Algebra 27, No. 9, 4117-4172 (1999). Reviewer: Blas Torrecillas (Almeria) MSC: 16W30 16S40 16W35 17B37 PDFBibTeX XMLCite \textit{B. Drabant} et al., Commun. Algebra 27, No. 9, 4117--4172 (1999; Zbl 0951.16013) Full Text: DOI arXiv
Maes, Ann; Van Daele, Alfons Notes on compact quantum groups. (English) Zbl 0962.46054 Nieuw Arch. Wiskd., IV. Ser. 16, No. 1-2, 73-112 (1998). MSC: 46L89 17B37 16W30 PDFBibTeX XMLCite \textit{A. Maes} and \textit{A. Van Daele}, Nieuw Arch. Wiskd., IV. Ser. 16, No. 1--2, 73--112 (1998; Zbl 0962.46054) Full Text: arXiv
Van Daele, A. An algebraic framework for group duality. (English) Zbl 0933.16043 Adv. Math. 140, No. 2, 323-366 (1998). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 16W30 17B37 22D35 46L89 43A22 PDFBibTeX XMLCite \textit{A. Van Daele}, Adv. Math. 140, No. 2, 323--366 (1998; Zbl 0933.16043) Full Text: DOI
Kustermans, J.; Van Daele, A. \(C^*\)-algebraic quantum groups arising from algebraic quantum groups. (English) Zbl 1009.46038 Int. J. Math. 8, No. 8, 1067-1139 (1997). MSC: 46L89 17B37 46L05 16W30 PDFBibTeX XMLCite \textit{J. Kustermans} and \textit{A. Van Daele}, Int. J. Math. 8, No. 8, 1067--1139 (1997; Zbl 1009.46038) Full Text: DOI arXiv Backlinks: MO
Van Daele, A. The Haar measure on finite quantum groups. (English) Zbl 0888.16023 Proc. Am. Math. Soc. 125, No. 12, 3489-3500 (1997). Reviewer: E.J.Taft (New Brunswick) MSC: 16W30 17B37 PDFBibTeX XMLCite \textit{A. Van Daele}, Proc. Am. Math. Soc. 125, No. 12, 3489--3500 (1997; Zbl 0888.16023) Full Text: DOI
Van Daele, A. Multiplier Hopf algebras and duality. (English) Zbl 0872.17008 Budzyński, Robert (ed.) et al., Quantum groups and quantum spaces. Lectures delivered during the minisemester, Warsaw, Poland, December 1, 1995. Warszawa: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 40, 51-58 (1997). MSC: 17B37 46L89 16W30 22D35 PDFBibTeX XMLCite \textit{A. Van Daele}, Banach Cent. Publ. 40, 51--58 (1997; Zbl 0872.17008)
Van Daele, A.; Woronowicz, S. L. Duality for the quantum \(E(2)\) group. (English) Zbl 0868.17013 Pac. J. Math. 173, No. 2, 375-385 (1996). Reviewer: A.Van Daele (Leuven) MSC: 17B37 16W30 46L89 PDFBibTeX XMLCite \textit{A. Van Daele} and \textit{S. L. Woronowicz}, Pac. J. Math. 173, No. 2, 375--385 (1996; Zbl 0868.17013) Full Text: DOI
Van Daele, Alfons; Wang, Shuzhou Universal quantum groups. (English) Zbl 0870.17011 Int. J. Math. 7, No. 2, 255-263 (1996). MSC: 17B37 46L89 PDFBibTeX XMLCite \textit{A. Van Daele} and \textit{S. Wang}, Int. J. Math. 7, No. 2, 255--263 (1996; Zbl 0870.17011) Full Text: DOI
Van Daele, A. Discrete quantum groups. (English) Zbl 0864.17012 J. Algebra 180, No. 2, 431-444 (1996). Reviewer: J.-P.Pier (Luxembourg) MSC: 17B37 16W30 46L89 PDFBibTeX XMLCite \textit{A. Van Daele}, J. Algebra 180, No. 2, 431--444 (1996; Zbl 0864.17012) Full Text: DOI
Van Daele, A. The Haar measure on a compact quantum group. (English) Zbl 0844.46032 Proc. Am. Math. Soc. 123, No. 10, 3125-3128 (1995). MSC: 46L05 81R50 22C05 16W30 46L55 PDFBibTeX XMLCite \textit{A. Van Daele}, Proc. Am. Math. Soc. 123, No. 10, 3125--3128 (1995; Zbl 0844.46032) Full Text: DOI
Van Daele, A.; Van Keer, S. The Yang-Baxter and pentagon equation. (English) Zbl 0811.17014 Compos. Math. 91, No. 2, 201-221 (1994). Reviewer: S.Khoroshkin (Moskva) MSC: 17B37 16W30 46L99 81R50 PDFBibTeX XMLCite \textit{A. Van Daele} and \textit{S. Van Keer}, Compos. Math. 91, No. 2, 201--221 (1994; Zbl 0811.17014) Full Text: Numdam EuDML
Van Daele, A. Multiplier Hopf algebras. (English) Zbl 0809.16047 Trans. Am. Math. Soc. 342, No. 2, 917-932 (1994). Reviewer: Li Fang (Nanjing) MSC: 16W30 17B37 PDFBibTeX XMLCite \textit{A. Van Daele}, Trans. Am. Math. Soc. 342, No. 2, 917--932 (1994; Zbl 0809.16047) Full Text: DOI Backlinks: MO
Van Daele, Alfons Dual pairs of Hopf *-algebras. (English) Zbl 0796.16034 Bull. Lond. Math. Soc. 25, No. 3, 209-230 (1993). Reviewer: A.Van Daele (Heverlee) MSC: 16W30 17B37 PDFBibTeX XMLCite \textit{A. Van Daele}, Bull. Lond. Math. Soc. 25, No. 3, 209--230 (1993; Zbl 0796.16034) Full Text: DOI
Van Daele, A. Quantum deformation of the Heisenberg group. (English) Zbl 0811.46074 Araki, H. (ed.) et al., Proceedings of the satellite conference of ICM-90: Current topics in operator algebras, Nara-ken New Public Hall, Japan, 16-19 August 1990. Singapore: World Scientific. 314-325 (1991). MSC: 46L60 PDFBibTeX XMLCite \textit{A. Van Daele}, in: Proceedings of the satellite conference of ICM-90: Current topics in operator algebras, Nara-ken New Public Hall, Japan, 16-19 August 1990. Singapore: World Scientific. 314--325 (1991; Zbl 0811.46074)