Kharchenko, V. K.; Díaz Sosa, M. L. Combinatorial rank of quantum groups of infinite series. (English) Zbl 1448.20040 Shum, K. P. (ed.) et al., New trends in algebras and combinatorics. Proceedings of the 3rd international congress in algebras and combinatorics, ICAC 2017, Hong Kong, China, August 25–28, 2017. In honor of Professor Leonid Bokut on the occasion of his 80th birthday. Hackensack, NJ: World Scientific. 228-254 (2020). MSC: 20G42 17B37 PDFBibTeX XMLCite \textit{V. K. Kharchenko} and \textit{M. L. Díaz Sosa}, in: New trends in algebras and combinatorics. Proceedings of the 3rd international congress in algebras and combinatorics, ICAC 2017, Hong Kong, China, August 25--28, 2017. In honor of Professor Leonid Bokut on the occasion of his 80th birthday. Hackensack, NJ: World Scientific. 228--254 (2020; Zbl 1448.20040) Full Text: DOI
Kharchenko, V. K. Quantizations \(U_q (\mathfrak{sl}_{n + 1}^+)\) and \(U_q (\mathfrak{so}_{2n + 1}^+)\) as quadratic-linear algebras. (English) Zbl 1468.17023 J. Algebra 564, 412-435 (2020). Reviewer: Dmitry Artamonov (Moskva) MSC: 17B37 16T05 16T20 16Z10 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, J. Algebra 564, 412--435 (2020; Zbl 1468.17023) Full Text: DOI
Kharchenko, V. K.; Vay, C. Explicit coproduct formulas for quantum group of the type \(G_2\). (English) Zbl 1480.17017 J. Algebra 500, 103-116 (2018). MSC: 17B37 PDFBibTeX XMLCite \textit{V. K. Kharchenko} and \textit{C. Vay}, J. Algebra 500, 103--116 (2018; Zbl 1480.17017) Full Text: DOI arXiv
Díaz Sosa, M. L.; Kharchenko, V. Combinatorial rank of \(u_q(\mathfrak{so}_{2n})\). (English) Zbl 1395.17025 J. Algebra 448, 48-73 (2016). MSC: 17B37 16T05 16T20 PDFBibTeX XMLCite \textit{M. L. Díaz Sosa} and \textit{V. Kharchenko}, J. Algebra 448, 48--73 (2016; Zbl 1395.17025) Full Text: DOI
Kharchenko, V. K. Explicit coproduct formula for quantum groups of infinite series. (English) Zbl 1395.16040 Isr. J. Math. 208, 13-43 (2015). MSC: 16T20 16S10 17B37 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, Isr. J. Math. 208, 13--43 (2015; Zbl 1395.16040) Full Text: DOI arXiv
Kharchenko, Vladislav Quantum Lie theory. A multilinear approach. (English) Zbl 1337.17001 Lecture Notes in Mathematics 2150. Cham: Springer (ISBN 978-3-319-22703-0/pbk; 978-3-319-22704-7/ebook). xiii, 302 p. (2015). Reviewer: Isar Rober Goyvaerts (Torino) MSC: 17-02 16-02 16T20 17B37 PDFBibTeX XMLCite \textit{V. Kharchenko}, Quantum Lie theory. A multilinear approach. Cham: Springer (2015; Zbl 1337.17001) Full Text: DOI
Kharchenko, V. K. Quantizations of Kac-Moody algebras. (English) Zbl 1344.16030 J. Pure Appl. Algebra 218, No. 4, 666-683 (2014). MSC: 16T20 17B37 17B67 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, J. Pure Appl. Algebra 218, No. 4, 666--683 (2014; Zbl 1344.16030) Full Text: DOI
Kharchenko, V. K.; Shestakov, I. P. Generalizations of Lie algebras. (English) Zbl 1263.17006 Adv. Appl. Clifford Algebr. 22, No. 3, 721-743 (2012). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 17B05 17B37 17B75 16T05 16T20 PDFBibTeX XMLCite \textit{V. K. Kharchenko} and \textit{I. P. Shestakov}, Adv. Appl. Clifford Algebr. 22, No. 3, 721--743 (2012; Zbl 1263.17006) Full Text: DOI
Kharchenko, V. K.; Diaz Sosa, M. L. Computing of the combinatorial rank of \(u_{q}(\mathfrak {so}_{2n+1})\). (English) Zbl 1305.17012 Commun. Algebra 39, No. 12, 4705-4718 (2011). Reviewer: Yang Shilin (Beijing) MSC: 17B37 16T05 16T20 PDFBibTeX XMLCite \textit{V. K. Kharchenko} and \textit{M. L. Diaz Sosa}, Commun. Algebra 39, No. 12, 4705--4718 (2011; Zbl 1305.17012) Full Text: DOI
Kharchenko, V. K.; Lara Sagahon, A. V.; Garza Rivera, J. L. Computing of the number of right coideal subalgebras of \(U_q(\mathfrak{so}_{2n+1})\). (English) Zbl 1259.17012 J. Algebra 341, No. 1, 279-296 (2011); corrigendum 354, No. 1, 224-225 (2012). Reviewer: Olaf Ninnemann (Uffing am Staffelsee) MSC: 17B37 16T05 17-08 PDFBibTeX XMLCite \textit{V. K. Kharchenko} et al., J. Algebra 341, No. 1, 279--296 (2011; Zbl 1259.17012) Full Text: DOI DOI
Kharchenko, V. K. Right coideal subalgebras of \(U_q^+(\mathfrak{so}_{2n+1})\). (English) Zbl 1229.17016 J. Eur. Math. Soc. (JEMS) 13, No. 6, 1677-1735 (2011). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 17B37 16T05 16T20 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, J. Eur. Math. Soc. (JEMS) 13, No. 6, 1677--1735 (2011; Zbl 1229.17016) Full Text: DOI arXiv
Kharchenko, V. K. Triangular decomposition of right coideal subalgebras. (English) Zbl 1217.17009 J. Algebra 324, No. 11, 3048-3089 (2010). Reviewer: Chen Yong-Qing (Shenzhen) MSC: 17B37 17B67 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, J. Algebra 324, No. 11, 3048--3089 (2010; Zbl 1217.17009) Full Text: DOI arXiv
Kharchenko, V. K. PBW-bases of coideal subalgebras and a freeness theorem. (English) Zbl 1165.16023 Trans. Am. Math. Soc. 360, No. 10, 5121-5143 (2008). Reviewer: Earl J. Taft (New Brunswick) MSC: 16W30 16W35 17B37 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, Trans. Am. Math. Soc. 360, No. 10, 5121--5143 (2008; Zbl 1165.16023) Full Text: DOI
Kharchenko, V. K.; Lara Sagahon, A. V. Right coideal subalgebras in \(U_q(\mathfrak{sl}_{n+1})\). (English) Zbl 1186.17008 J. Algebra 319, No. 6, 2571-2625 (2008). Reviewer: Nicolás Andruskiewitsch (Cordoba) MSC: 17B37 16T05 16T20 PDFBibTeX XMLCite \textit{V. K. Kharchenko} and \textit{A. V. Lara Sagahon}, J. Algebra 319, No. 6, 2571--2625 (2008; Zbl 1186.17008) Full Text: DOI
Kharchenko, V. K. Connected braided Hopf algebras. (English) Zbl 1115.16021 J. Algebra 307, No. 1, 24-48 (2007). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 16W30 17B35 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, J. Algebra 307, No. 1, 24--48 (2007; Zbl 1115.16021) Full Text: DOI
Kharchenko, V.; Sagahon, A. V. Lara Right coideal subalgebras in \(U_q(\frak{sl}_{n+1}).\). arXiv:0710.2143 Preprint, arXiv:0710.2143 [math.QA] (2007). MSC: 16W30 17B37 BibTeX Cite \textit{V. Kharchenko} and \textit{A. V. L. Sagahon}, ``Right coideal subalgebras in $U_q(\frak{sl}_{n+1}).$'', Preprint, arXiv:0710.2143 [math.QA] (2007) Full Text: arXiv
Kharchenko, V. K. On right coideal subalgebras. arXiv:math/0702504 Preprint, arXiv:math/0702504 [math.QA] (2007). MSC: 16W30 17B37 BibTeX Cite \textit{V. K. Kharchenko}, ``On right coideal subalgebras'', Preprint, arXiv:math/0702504 [math.QA] (2007) Full Text: arXiv
Filippov, V. T.; Kharchenko, V. K.; Shestakov, I. P. Dniester notebook: unsolved problems in the theory of rings and modules. (English) Zbl 1288.16001 Sabinin, Lev V. (ed.) et al., Non-associative algebra and its applications. Proceedings of the 5th international conference, Oaxtep, Mexico, July 27–August 2, 2003. Boca Raton, FL: Chapman & Hall/CRC (ISBN 0-8247-2669-3/pbk). Lecture Notes in Pure and Applied Mathematics 246, 461-504 (2006). MSC: 16-02 17-02 00A07 PDFBibTeX XMLCite \textit{V. T. Filippov} et al., Lect. Notes Pure Appl. Math. 246, 461--504 (2006; Zbl 1288.16001)
Bokut, L.; Kharchenko, V.; Lõhmus, J.; Moreno, G.; Nesterov, A.; Rosenbaum, M.; Shestakov, I. Obituary: Lev Vasilievich Sabinin (June 21, 1932 – June 4, 2004). (English) Zbl 1321.01045 Sabinin, Lev V. (ed.) et al., Non-associative algebra and its applications. Proceedings of the 5th international conference, Oaxtep, Mexico, July 27–August 2, 2003. Boca Raton, FL: Chapman & Hall/CRC (ISBN 0-8247-2669-3/pbk). Lecture Notes in Pure and Applied Mathematics 246, xi-xxiii (2006). MSC: 01A70 17-03 PDFBibTeX XMLCite \textit{L. Bokut} et al., Lect. Notes Pure Appl. Math. 246, xi-xxiii (2006; Zbl 1321.01045)
Kharchenko, V. K. Braided version of Shirshov-Witt theorem. (English) Zbl 1082.17005 J. Algebra 294, No. 1, 196-225 (2005). Reviewer: Vesselin Drensky (Sofia) MSC: 17B01 17B35 17B60 16S10 16W30 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, J. Algebra 294, No. 1, 196--225 (2005; Zbl 1082.17005) Full Text: DOI
Kharchenko, V. K.; Andrade Álvarez, A. On the combinatorial rank of Hopf algebras. (English) Zbl 1143.16305 de la Peña, José A. (ed.) et al., Algebraic structures and their representations. Proceedings of ‘XV coloquio Latinoamericano de álgebra’, Cocoyoc, Morelos, México, July 20–26, 2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3630-7/pbk). Contemporary Mathematics 376, 299-308 (2005). MSC: 16W30 16W35 17B37 PDFBibTeX XMLCite \textit{V. K. Kharchenko} and \textit{A. Andrade Álvarez}, Contemp. Math. 376, 299--308 (2005; Zbl 1143.16305)
Kharchenko, V. K. Quantum Lie algebras and related problems. (English) Zbl 1041.17014 Fong, Yuen (ed.) et al., Proceedings of the 3rd international algebra conference, Tainan, Taiwan, June 16–July 1, 2002. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1442-2/hbk). 67-114 (2003). Reviewer: Paul M. Cohn (London) MSC: 17B37 16W30 16W35 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, in: Proceedings of the 3rd international algebra conference, Tainan, Taiwan, June 16--July 1, 2002. Dordrecht: Kluwer Academic Publishers. 67--114 (2003; Zbl 1041.17014)
Kharchenko, V. K. Constants of coordinate differential calculi defined by Yang-Baxter operators. (English) Zbl 1040.17009 J. Algebra 267, No. 1, 96-129 (2003). Reviewer: Nicolás Andruskiewitsch (Cordoba) MSC: 17B37 58B32 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, J. Algebra 267, No. 1, 96--129 (2003; Zbl 1040.17009) Full Text: DOI
Kharchenko, V. K. A combinatorial approach to the quantification of Lie algebras. (English) Zbl 1069.17008 Pac. J. Math. 203, No. 1, 191-233 (2002). MSC: 17B37 16W30 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, Pac. J. Math. 203, No. 1, 191--233 (2002; Zbl 1069.17008) Full Text: DOI arXiv
Kharchenko, V. K. Skew primitive elements in Hopf algebras and related identities. (English) Zbl 0987.16031 J. Algebra 238, No. 2, 534-559 (2001). Reviewer: Earl J.Taft (New Brunswick) MSC: 16W30 17B37 16S30 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, J. Algebra 238, No. 2, 534--559 (2001; Zbl 0987.16031) Full Text: DOI
Kharchenko, V. K. Multilinear quantum Lie operations. (English. Russian original) Zbl 1106.17019 J. Math. Sci., New York 116, No. 1, 3063-3073 (2003); translation from Zap. Nauchn. Semin. POMI 272, 321-340 (2000). MSC: 17B37 16W35 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, J. Math. Sci., New York 116, No. 1, 3063--3073 (2000; Zbl 1106.17019); translation from Zap. Nauchn. Semin. POMI 272, 321--340 (2000) Full Text: DOI arXiv
Kharchenko, V. K. An Algebra of Skew Primitive Elements. arXiv:math/0006077 Preprint, arXiv:math/0006077 [math.QA] (2000). MSC: 16Wxx 17Bxx BibTeX Cite \textit{V. K. Kharchenko}, ``An Algebra of Skew Primitive Elements'', Preprint, arXiv:math/0006077 [math.QA] (2000) Full Text: arXiv
Kharchenko, V. K. Character Hopf algebras and quantizations of Lie algebras. (English. Russian original) Zbl 1050.16501 Dokl. Math. 60, No. 3, 328-329 (1999); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 369, No. 1, 22-23 (1999). MSC: 16W30 17B37 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, Dokl. Math. 60, No. 3, 22--23 (1999; Zbl 1050.16501); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 369, No. 1, 22--23 (1999)
Kharchenko, V. K. A quantum analog of the Poincaré-Birkhoff-Witt theorem. (English. Russian original) Zbl 0936.16034 Algebra Logika 38, No. 4, 476-507 (1999); translation in Algebra Logic 38, No. 4, 259-276 (1999). Reviewer: K.N.Ponomarev (Novosibirsk) MSC: 16W30 17B37 16S30 16W35 17B35 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, Algebra Logika 38, No. 4, 476--507 (1999; Zbl 0936.16034); translation in Algebra Logic 38, No. 4, 259--276 (1999) Full Text: arXiv EuDML
Kharchenko, V. K. An existence condition for multilinear quantum operations. (English) Zbl 0943.17016 J. Algebra 217, No. 1, 188-228 (1999). Reviewer: Ye Jiachen (Shanghai) MSC: 17B37 16W30 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, J. Algebra 217, No. 1, 188--228 (1999; Zbl 0943.17016) Full Text: DOI
Kharchenko, V. K. The algebra of skew primitive elements. (English. Russian original) Zbl 0917.16017 Algebra Logika 37, No. 2, 181-223 (1998); translation in Algebra Logic 37, No. 2, 101-126 (1998). Reviewer: A.P.Pozhidaev (Novosibirsk) MSC: 16W30 17B37 08A55 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, Algebra Logika 37, No. 2, 181--223 (1998; Zbl 0917.16017); translation in Algebra Logic 37, No. 2, 101--126 (1998)
Borowiec, Andrzej; Kharchenko, Vladislav; Oziewicz, Zbigniew First order calculi with values in right-universal bimodules. (English) Zbl 0878.16017 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, 171-184 (1997). Reviewer: A.A.Bogush (Minsk) MSC: 16W25 46L85 46L87 16D20 17B37 16U80 PDFBibTeX XMLCite \textit{A. Borowiec} et al., Banach Cent. Publ. 40, 171--184 (1997; Zbl 0878.16017) Full Text: arXiv
Borowiec, A.; Kharchenko, V. K. Algebraic approach to calculuses with partial derivatives. (English) Zbl 0852.16027 Sib. Adv. Math. 5, No. 2, 10-37 (1995). MSC: 16W25 46L85 46L87 17B37 PDFBibTeX XMLCite \textit{A. Borowiec} and \textit{V. K. Kharchenko}, Sib. Adv. Math. 5, No. 2, 10--37 (1995; Zbl 0852.16027)
Borowiec, Andrzej; Kharchenko, Vladislav K. First order optimum calculi. (English) Zbl 0883.16024 Bull. Soc. Sci. Lett. Łódź 45, Sér. Rech. Déform. 19, 75-88 (1995). MSC: 16W25 17B37 16D20 46L85 46L87 17B66 PDFBibTeX XMLCite \textit{A. Borowiec} and \textit{V. K. Kharchenko}, Bull. Soc. Sci. Lett. Łódź, Sér. Rech. Déform. 45(19), 75--88 (1995; Zbl 0883.16024) Full Text: arXiv
Borowiec, A.; Kharchenko, V. K. Coordinate calculi on associative algebras. (English) Zbl 0879.16023 Lukierski, Jerzy (ed.) et al., Quantum groups: formalism and applications. Proceedings of the XXX Karpacz winter school of theoretical physics, Karpacz, Poland, February 14–26, 1994. Warszawa: PWN-Polish Scientific Publishers. 231-241 (1995). Reviewer: P.Šťovíček (Praha) MSC: 16W25 46L85 46L87 17B37 16W50 PDFBibTeX XMLCite \textit{A. Borowiec} and \textit{V. K. Kharchenko}, in: Quantum groups: formalism and applications. Proceedings of the XXX Karpacz winter school of theoretical physics, Karpacz, Poland, February 14--26, 1994. Warszawa: PWN-Polish Scientific Publishers. 231--241 (1995; Zbl 0879.16023) Full Text: arXiv
Filippov, V. T. (ed.); Kharchenko, V. K. (ed.); Shestakov, I. P. (ed.) The Dniester notebook. Unsolved problems in the theory of rings and modules. 4th ed. (Днестровская тетрад’. Нерешенные проблемы теории колец и модулей.) (Russian) Zbl 0868.16001 Novosibirsk: Institut Matematiki SO RAN, 74 p. (1993). MSC: 16-02 17-02 00A07 PDFBibTeX XMLCite \textit{V. T. Filippov} (ed.) et al., Днестровская тетрад'. Нерешенные проблемы теории колец и модулей (Russian). 4th ed. Novosibirsk: Institut Matematiki SO RAN (1993; Zbl 0868.16001)
Kharchenko, V. K. Constants of derivations of prime rings. (English) Zbl 0483.16032 Math. USSR, Izv. 18, 381-401 (1982). MSC: 16W20 16N60 16Rxx 17B40 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, Math. USSR, Izv. 18, 381--401 (1982; Zbl 0483.16032) Full Text: DOI
Kharchenko, V. K. Constants of derivations of primary rings. (Russian) Zbl 0469.16019 Izv. Akad. Nauk SSSR, Ser. Mat. 45, 435-462 (1981). MSC: 16W20 16N60 16Rxx 17B40 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, Izv. Akad. Nauk SSSR, Ser. Mat. 45, 435--462 (1981; Zbl 0469.16019)
Kharchenko, V. K. The actions of groups and Lie algebras on non-commutative rings. (English) Zbl 0459.16023 Russ. Math. Surv. 35, No. 2, 77-104 (1980). MSC: 16W20 16Rxx 17B40 13N05 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, Russ. Math. Surv. 35, No. 2, 77--104 (1980; Zbl 0459.16023) Full Text: DOI
Kharchenko, V. K. Actions of groups and Lie algebras on non-commutative rings. (Russian) Zbl 0435.16018 Usp. Mat. Nauk 35, No. 2(212), 67-90 (1980). MSC: 16W20 16Rxx 17B40 13N05 PDFBibTeX XMLCite \textit{V. K. Kharchenko}, Usp. Mat. Nauk 35, No. 2(212), 67--90 (1980; Zbl 0435.16018)