Yu. I. Manin, “Notes on quantum groups and quantum de Rham complexes”, TMF, 92:3 (1992), 425–450; Theoret. and Math. Phys., 92:3 (1992), 997

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Teoreticheskaya i Matematicheskaya Fizika, 1992, Volume 92, Number 3, Pages 425–450 (Mi tmf1513)

This article is cited in 30 scientific papers (total in 31 papers)

Notes on quantum groups and quantum de Rham complexes

Yu. I. Manin

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (2286 kB) Citations (31)

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Abstract: De Rham complexes of quantum spaces and quantum groups are studied by means of extension of “universal co-action” technique to the differential algebras.

Received: 17.06.1992

English version:
Theoretical and Mathematical Physics, 1992, Volume 92, Issue 3, Pages 997–1019
DOI: https://doi.org/10.1007/BF01017077

Bibliographic databases:

Document Type: Article

Language: English

Citation: Yu. I. Manin, “Notes on quantum groups and quantum de Rham complexes”, TMF, 92:3 (1992), 425–450; Theoret. and Math. Phys., 92:3 (1992), 997–1019

Citation in format AMSBIB

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\transl

\jour Theoret. and Math. Phys.

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\pages 997--1019

\crossref{https://doi.org/10.1007/BF01017077}

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Linking options:

https://www.mathnet.ru/eng/tmf1513

https://www.mathnet.ru/eng/tmf/v92/i3/p425

This publication is cited in the following 31 articles:

Naihuan Jing, Jian Zhang, “Minor identities for Sklyanin determinants”, Advances in Mathematics, 442 (2024), 109569
Vladislav Kupriyanov, Alexey Sharapov, “What is the Seiberg–Witten map exactly?”, J. Phys. A: Math. Theor., 56:37 (2023), 375201
A. V. Silantev, “Kvantovaya teoriya predstavlenii i matritsy Manina I: konechnomernyi sluchai”, Tr. MMO, 83, no. 1, MTsNMO, M., 2022, 87–179
A. V. Silantyev, “Quantum representation theory and Manin matrices I: The finite-dimensional case”, Trans. Moscow Math. Soc., –
Alexey Silantyev, “Manin Matrices for Quadratic Algebras”, SIGMA, 17 (2021), 066, 81 pp.
Ogievetsky O. Pyatov P., “Quantum Matrix Algebras of Bmw Type: Structure of the Characteristic Subalgebra”, J. Geom. Phys., 162 (2021), 104086
Naihuan Jing, Jian Zhang, Progress in Mathematics, 337, Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification, 2021, 427
Salih Celik, “Left-covariant differential calculi on GL̃q(2)”, Journal of Mathematical Physics, 62:7 (2021), 073504
Andrey Glubokov, “Ideals on the Quantum Plane's Jet Space”, Mathematics, 8:3 (2020), 352
Salih Celik, “Quantum de Rham complex on 𝔸h1|2”, J. Algebra Appl., 19:09 (2020), 2050177
Naihuan Jing, Jian Zhang, “Quantum hyperdeterminants and hyper-Pfaffians”, Math. Z., 287:3-4 (2017), 897
Naihuan Jing, Jian Zhang, “Quantum Permanents and Hafnians via Pfaffians”, Lett Math Phys, 106:10 (2016), 1451
Gu H. Hu N., “Loewy Filtration and Quantum de Rham Cohomology Over Quantum Divided Power Algebra”, J. Algebra, 435 (2015), 1–32
A. M. Semikhatov, “Quantum $s\ell(2)$ action on a divided-power quantum plane at even roots of unity”, Theoret. and Math. Phys., 164:1 (2010), 853–868
A. M. Semikhatov, “A differential $\mathscr U$-module algebra for $\mathscr{U}=\overline{\mathscr U}_{\mathfrak{q}}s\ell(2)$ at an even root of unity”, Theoret. and Math. Phys., 159:1 (2009), 424–447
A. Chervov, G. Falqui, V. Rubtsov, “Algebraic properties of Manin matrices 1”, Advances in Applied Mathematics, 43:3 (2009), 239
A Dimakis, F Müller-Hoissen, “Automorphisms of associative algebras and noncommutative geometry”, J. Phys. A: Math. Gen., 37:6 (2004), 2307
A. P. Isaev, O. V. Ogievetskii, “BRST Operator for Quantum Lie Algebras and Differential Calculus on Quantum Groups”, Theoret. and Math. Phys., 129:2 (2001), 1558–1572
A.P. Isaev, O.V. Ogievetsky, “BRST and anti-BRST operators for quantum linear algebra Uq(gl(N)).”, Nuclear Physics B - Proceedings Supplements, 102-103 (2001), 306
Andrzej Borowiec, Władysław Marcinek, “On crossed product of algebras”, Journal of Mathematical Physics, 41:10 (2000), 6959

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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