Greenberg, Zachary; Kaufman, Dani; Wienhard, Anna \(\mathrm{SL}_2\)-like Properties of Matrices Over Noncommutative Rings and Generalizations of Markov Numbers. arXiv:2402.19300 Preprint, arXiv:2402.19300 [math.RA] (2024). MSC: 15B33 16W10 13F60 20G42 BibTeX Cite \textit{Z. Greenberg} et al., ``$\mathrm{SL}_2$-like Properties of Matrices Over Noncommutative Rings and Generalizations of Markov Numbers'', Preprint, arXiv:2402.19300 [math.RA] (2024) Full Text: arXiv OA License
Inoue, Rei; Yamazaki, Takao Invariants of Weyl group action and \(q\)-characters of quantum affine algebras. (English) Zbl 07788004 Algebr. Represent. Theory 26, No. 6, 3167-3183 (2023). Reviewer: Enrico Jabara (Venezia) MSC: 17B37 20G42 13F60 17B10 PDFBibTeX XMLCite \textit{R. Inoue} and \textit{T. Yamazaki}, Algebr. Represent. Theory 26, No. 6, 3167--3183 (2023; Zbl 07788004) Full Text: DOI arXiv
Martello, Davide Dal; Mazzocco, Marta Generalized double affine Hecke algebras, their representations and higher Teichmüller theory. arXiv:2307.06803 Preprint, arXiv:2307.06803 [math.QA] (2023). MSC: 20G42 17B37 20C08 13F60 BibTeX Cite \textit{D. D. Martello} and \textit{M. Mazzocco}, ``Generalized double affine Hecke algebras, their representations and higher Teichm\"uller theory'', Preprint, arXiv:2307.06803 [math.QA] (2023) Full Text: arXiv OA License
Fujita, Ryo; Hernandez, David; Oh, Se-jin; Oya, Hironori Isomorphisms among quantum Grothendieck rings and cluster algebras. arXiv:2304.02562 Preprint, arXiv:2304.02562 [math.RT] (2023). MSC: 17B37 13F60 20G42 81R50 17B10 17B67 BibTeX Cite \textit{R. Fujita} et al., ``Isomorphisms among quantum Grothendieck rings and cluster algebras'', Preprint, arXiv:2304.02562 [math.RT] (2023) Full Text: arXiv OA License
Ringel, Claus Michael; Zhang, Pu Gorenstein-projective modules over short local algebras. (English) Zbl 07730819 J. Lond. Math. Soc., II. Ser. 106, No. 2, 528-589 (2022). Reviewer: Zhibing Zhao (Hefei) MSC: 16G10 13D07 16E65 16G50 20G42 PDFBibTeX XMLCite \textit{C. M. Ringel} and \textit{P. Zhang}, J. Lond. Math. Soc., II. Ser. 106, No. 2, 528--589 (2022; Zbl 07730819) Full Text: DOI arXiv
Jensen, Bernt Tore; King, Alastair; Su, Xiuping Categorification and the quantum Grassmannian. (English) Zbl 1503.13012 Adv. Math. 406, Article ID 108577, 29 p. (2022). Reviewer: Matthew Pressland (Glasgow) MSC: 13F60 14M15 16G50 20G42 PDFBibTeX XMLCite \textit{B. T. Jensen} et al., Adv. Math. 406, Article ID 108577, 29 p. (2022; Zbl 1503.13012) Full Text: DOI arXiv
Alekseev, Anton; Berenstein, Arkady; Hoffman, Benjamin; Li, Yanpeng Langlands duality and Poisson-Lie duality via cluster theory and tropicalization. (English) Zbl 1484.22007 Sel. Math., New Ser. 27, No. 4, Paper No. 69, 54 p. (2021). MSC: 22E15 13F60 14T20 20G42 53D17 PDFBibTeX XMLCite \textit{A. Alekseev} et al., Sel. Math., New Ser. 27, No. 4, Paper No. 69, 54 p. (2021; Zbl 1484.22007) Full Text: DOI arXiv
Ringel, Claus Michael; Zhang, Pu Koszul modules (and the \(\Omega\)-growth of modules) over short local algebras. (English) Zbl 1492.16011 J. Pure Appl. Algebra 225, No. 12, Article ID 106772, 19 p. (2021). MSC: 16G10 16S37 13D07 16E65 16G50 20G42 PDFBibTeX XMLCite \textit{C. M. Ringel} and \textit{P. Zhang}, J. Pure Appl. Algebra 225, No. 12, Article ID 106772, 19 p. (2021; Zbl 1492.16011) Full Text: DOI arXiv
Inoue, Rei Cluster realization of Weyl groups and \(q\)-characters of quantum affine algebras. (English) Zbl 1454.13033 Lett. Math. Phys. 111, No. 1, Paper No. 4, 32 p. (2021). MSC: 13F60 17B22 20G42 PDFBibTeX XMLCite \textit{R. Inoue}, Lett. Math. Phys. 111, No. 1, Paper No. 4, 32 p. (2021; Zbl 1454.13033) Full Text: DOI arXiv
Inoue, Rei Cluster realization of Weyl groups. (Japanese. English summary) Zbl 1455.13038 RIMS Kôkyûroku Bessatsu B78, 225-233 (2020). MSC: 13F60 20F55 16G20 17B22 20G42 PDFBibTeX XMLCite \textit{R. Inoue}, RIMS Kôkyûroku Bessatsu B78, 225--233 (2020; Zbl 1455.13038) Full Text: Link
Goodearl, Kenneth R.; Yakimov, M. T. The Berenstein-Zelevinsky quantum cluster algebra conjecture. (English) Zbl 1471.13046 J. Eur. Math. Soc. (JEMS) 22, No. 8, 2453-2509 (2020). MSC: 13F60 20G42 16T20 17B37 14M15 PDFBibTeX XMLCite \textit{K. R. Goodearl} and \textit{M. T. Yakimov}, J. Eur. Math. Soc. (JEMS) 22, No. 8, 2453--2509 (2020; Zbl 1471.13046) Full Text: DOI arXiv
Genz, Volker; Koshevoy, Gleb; Schumann, Bea Polyhedral parametrizations of canonical bases & cluster duality. (English) Zbl 1453.13065 Adv. Math. 369, Article ID 107178, 40 p. (2020). MSC: 13F60 14J33 17B37 20G42 PDFBibTeX XMLCite \textit{V. Genz} et al., Adv. Math. 369, Article ID 107178, 40 p. (2020; Zbl 1453.13065) Full Text: DOI arXiv
Brito, Matheus; Chari, Vyjayanthi Tensor products and \(q\)-characters of HL-modules and monoidal categorifications. (Produits tensoriels et \(Q\)-caractères de HL-modules et catégorifications monoïdales.) (English. French summary) Zbl 1446.17026 J. Éc. Polytech., Math. 6, 581-619 (2019). MSC: 17B37 13F60 18M99 20G42 PDFBibTeX XMLCite \textit{M. Brito} and \textit{V. Chari}, J. Éc. Polytech., Math. 6, 581--619 (2019; Zbl 1446.17026) Full Text: DOI arXiv
Oya, Hironori The Chamber Ansatz for quantum unipotent cells. (English) Zbl 1454.13036 Transform. Groups 24, No. 1, 193-217 (2019). Reviewer: Thorsten Heidersdorf (Bonn) MSC: 13F60 17B37 16T20 20G42 PDFBibTeX XMLCite \textit{H. Oya}, Transform. Groups 24, No. 1, 193--217 (2019; Zbl 1454.13036) Full Text: DOI arXiv
Mészáros, Szabolcs Cocommutative elements form a maximal commutative subalgebra in quantum matrices. (English) Zbl 1418.16020 J. Algebra Appl. 17, No. 9, Article ID 1850179, 16 p. (2018). MSC: 16T20 20G42 81R50 13A50 PDFBibTeX XMLCite \textit{S. Mészáros}, J. Algebra Appl. 17, No. 9, Article ID 1850179, 16 p. (2018; Zbl 1418.16020) Full Text: DOI arXiv
Jakobsen, Hans P. The center of \(\mathcal U_q(\mathfrak{n}_\omega)\). (English) Zbl 1429.17015 Commun. Algebra 46, No. 1, 262-282 (2018). MSC: 17B37 17A45 13F60 20G42 16T20 PDFBibTeX XMLCite \textit{H. P. Jakobsen}, Commun. Algebra 46, No. 1, 262--282 (2018; Zbl 1429.17015) Full Text: DOI arXiv
Kashiwara, Masaki; Kim, Myungho; Oh, Se-jin; Park, Euiyong Monoidal categories associated with strata of flag manifolds. (English) Zbl 1437.17005 Adv. Math. 328, 959-1009 (2018). MSC: 17B37 20G42 13F60 20C08 PDFBibTeX XMLCite \textit{M. Kashiwara} et al., Adv. Math. 328, 959--1009 (2018; Zbl 1437.17005) Full Text: DOI arXiv
Kanakubo, Yuki Explicit forms of cluster variables on double Bruhat cells \(G^{u,e}\) of type B. (English) Zbl 1378.13013 Commun. Algebra 45, No. 9, 3825-3860 (2017). MSC: 13F60 20G42 PDFBibTeX XMLCite \textit{Y. Kanakubo}, Commun. Algebra 45, No. 9, 3825--3860 (2017; Zbl 1378.13013) Full Text: DOI arXiv
Kim, Hyun Kyu Phase constants in the Fock-Goncharov quantization of cluster varieties: long version. arXiv:1602.00361 Preprint, arXiv:1602.00361 [math.QA] (2016). MSC: 46L65 20G42 81R60 13F60 53D55 BibTeX Cite \textit{H. K. Kim}, ``Phase constants in the Fock-Goncharov quantization of cluster varieties: long version'', Preprint, arXiv:1602.00361 [math.QA] (2016) Full Text: arXiv OA License
Goodearl, Kenneth R.; Yakimov, Milen T. Unipotent and Nakayama automorphisms of quantum nilpotent algebras. (English) Zbl 1359.16036 Eisenbud, David (ed.) et al., Commutative algebra and noncommutative algebraic geometry. Volume II: Research articles. Cambridge: Cambridge University Press (ISBN 978-1-107-14972-4/hbk). Mathematical Sciences Research Institute Publications 68, 181-212 (2015). MSC: 16T20 13F60 16S36 16W20 20G42 PDFBibTeX XMLCite \textit{K. R. Goodearl} and \textit{M. T. Yakimov}, Math. Sci. Res. Inst. Publ. 68, 181--212 (2015; Zbl 1359.16036) Full Text: arXiv
Huang, Hau-Wen Finite-dimensional irreducible modules of the universal Askey-Wilson algebra. (English) Zbl 1331.33036 Commun. Math. Phys. 340, No. 3, 959-984 (2015). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33D45 06F25 13E15 17B37 20G42 PDFBibTeX XMLCite \textit{H.-W. Huang}, Commun. Math. Phys. 340, No. 3, 959--984 (2015; Zbl 1331.33036) Full Text: DOI arXiv
Rupel, Dylan The Feigin tetrahedron. (English) Zbl 1327.13082 SIGMA, Symmetry Integrability Geom. Methods Appl. 11, Paper 024, 30 p. (2015). MSC: 13F60 16G20 17B37 20G42 PDFBibTeX XMLCite \textit{D. Rupel}, SIGMA, Symmetry Integrability Geom. Methods Appl. 11, Paper 024, 30 p. (2015; Zbl 1327.13082) Full Text: DOI arXiv EMIS
Jakobsen, Hans Plesner; Pagani, Chiara Quantized matrix algebras and quantum seeds. (English) Zbl 1394.17037 Linear Multilinear Algebra 63, No. 4, 713-753 (2015). MSC: 17B37 20G42 13F60 PDFBibTeX XMLCite \textit{H. P. Jakobsen} and \textit{C. Pagani}, Linear Multilinear Algebra 63, No. 4, 713--753 (2015; Zbl 1394.17037) Full Text: DOI arXiv
Jakobsen, Hans P. Double Quantum Schubert Cells and Quantum Mutations. arXiv:1509.06137 Preprint, arXiv:1509.06137 [math.QA] (2015). MSC: 17B37 13F60 16T20 17A45 20G42 BibTeX Cite \textit{H. P. Jakobsen}, ``Double Quantum Schubert Cells and Quantum Mutations'', Preprint, arXiv:1509.06137 [math.QA] (2015) Full Text: arXiv OA License
Grabowski, Jan E.; Launois, Stéphane Graded quantum cluster algebras and an application to quantum Grassmannians. (English) Zbl 1315.13036 Proc. Lond. Math. Soc. (3) 109, No. 3, 697-732 (2014). Reviewer: Xueqing Chen (Whitewater) MSC: 13F60 20G42 17B37 PDFBibTeX XMLCite \textit{J. E. Grabowski} and \textit{S. Launois}, Proc. Lond. Math. Soc. (3) 109, No. 3, 697--732 (2014; Zbl 1315.13036) Full Text: DOI arXiv
Kimura, Yoshiyuki; Qin, Fan Graded quiver varieties, quantum cluster algebras and dual canonical basis. (English) Zbl 1331.13016 Adv. Math. 262, 261-312 (2014). Reviewer: Robert Marsh (Leeds) MSC: 13F60 16G20 18D10 20G42 PDFBibTeX XMLCite \textit{Y. Kimura} and \textit{F. Qin}, Adv. Math. 262, 261--312 (2014; Zbl 1331.13016) Full Text: DOI arXiv
Jakobsen, Hans Plesner; Zhang, Hechun Double-partition quantum cluster algebras. (English) Zbl 1291.13040 J. Algebra 372, 172-203 (2012). MSC: 13F60 16T20 17B37 16G20 20G42 PDFBibTeX XMLCite \textit{H. P. Jakobsen} and \textit{H. Zhang}, J. Algebra 372, 172--203 (2012; Zbl 1291.13040) Full Text: DOI arXiv
Kimura, Yoshiyuki Quantum unipotent subgroup and dual canonical basis. (English) Zbl 1282.17017 Kyoto J. Math. 52, No. 2, 277-331 (2012). MSC: 17B37 20G42 13F60 PDFBibTeX XMLCite \textit{Y. Kimura}, Kyoto J. Math. 52, No. 2, 277--331 (2012; Zbl 1282.17017) Full Text: DOI arXiv Euclid
Tran, Thao \(F\)-polynomials in quantum cluster algebras. (English) Zbl 1253.16016 Algebr. Represent. Theory 14, No. 6, 1025-1061 (2011). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 16G20 13F60 16S80 16T20 05E15 20G42 PDFBibTeX XMLCite \textit{T. Tran}, Algebr. Represent. Theory 14, No. 6, 1025--1061 (2011; Zbl 1253.16016) Full Text: DOI arXiv
Andersen, J. E.; Askitas, N.; Bar-Natan, D.; Baseilhac, S.; Benedetti, R.; Bigelow, S.; Boileau, M.; Bott, R.; Carter, J. S.; Deloup, F.; Dunfield, N.; Fenn, R.; Ferrand, E.; Garoufalidis, S.; Goussarov, M.; Guadagnini, E.; Habiro, H.; Hansen, S. K.; Harikae, T.; Haviv, A.; Jeong, M. -J.; Jones, V.; Kashaev, R.; Kawahigashi, Y.; Kerler, T.; Kidwell, M.; Kohno, T.; Kricker, A.; Le, T. T. Q.; Lescop, C.; Lin, X. -S.; Masbaum, G.; Massuyeau, G.; Morita, S.; Morton, H. R.; Murakami, H.; Murakami, J.; Nakanishi, Y.; Ohtsuki, T.; Ohyama, Y.; Okamoto, M.; Okuda, N.; Park, C. -Y.; Pilo, L.; Polyak, M.; Przytycki, J.; Roberts, J.; Rourke, C.; Rozansky, L.; Sanderson, B.; Sato, N.; Shinohara, Y.; Stanford, T.; Stoimenow, A.; Takata, T.; Thurston, D.; Turaev, V.; Viro, O.; Willerton, S.; Yokota, Y. Problems on invariants of knots and 3-manifolds. arXiv:math/0406190 Preprint, arXiv:math/0406190 [math.GT] (2004). MSC: 20F36 57M25 57M27 57R56 13B25 17B10 17B37 18D10 20C08 20G42 22E99 41A60 46L37 57M05 57M50 57N10 57Q10 81T18 81T45 BibTeX Cite \textit{J. E. Andersen} et al., ``Problems on invariants of knots and 3-manifolds'', Preprint, arXiv:math/0406190 [math.GT] (2004) Full Text: arXiv
Domokos, M.; Lenagan, T. H. Conjugation coinvariants of quantum matrices. (English) Zbl 1023.16022 Bull. Lond. Math. Soc. 35, No. 1, 117-127 (2003). MSC: 16R30 16W30 16W35 13A50 20G42 PDFBibTeX XMLCite \textit{M. Domokos} and \textit{T. H. Lenagan}, Bull. Lond. Math. Soc. 35, No. 1, 117--127 (2003; Zbl 1023.16022) Full Text: DOI