R∞-matrices, triangular l∞-bialgebras and quantum∞ groups

Denis Bashkirov; Alexander A Voronov

doi:10.1007/978-3-319-18212-4_2

R_∞-matrices, triangular l_∞-bialgebras and quantum_∞ groups

Denis Bashkirov, Alexander A Voronov

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

A homotopy analogue of the notion of a triangular Lie bialgebra is proposed with a goal of extending basic notions of the theory of quantum groups to the context of homotopy algebras and, in particular, introducing a homotopical generalization of the notion of a quantum group, or quantum_∞-group.

Original language	English (US)
Title of host publication	Geometric Methods in Physics - 33rd Workshop, 2014
Editors	Piotr Kielanowski, Pierre Bieliavsky, Anatol Odzijewicz, Martin Schlichenmaier, Theodore Voronov
Publisher	Springer International Publishing
Pages	39-47
Number of pages	9
ISBN (Print)	9783319182117
DOIs	https://doi.org/10.1007/978-3-319-18212-4_2
State	Published - 2015
Event	33rd Workshop on Geometric Methods in Physics, 2014 - Bialowieza, Poland Duration: Jun 29 2014 → Jul 5 2014

Publication series

Name	Trends in Mathematics
Volume	71
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Other

Other	33rd Workshop on Geometric Methods in Physics, 2014
Country/Territory	Poland
City	Bialowieza
Period	6/29/14 → 7/5/14

Bibliographical note

Publisher Copyright:
© 2015 Springer International Publishing Switzerland.

Keywords

Classical r-matrix
Co-Poisson-Hopf algebra
L-algebra
L-bialgebra
Lie bialgebra
Maurer-Cartan equation
Quantization
Quantum group
Triangular Lie bialgebra
Universal enveloping algebra
Yang-Baxter equation

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10.1007/978-3-319-18212-4_2

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Cite this

Bashkirov, D., & Voronov, A. A. (2015). R_∞-matrices, triangular l_∞-bialgebras and quantum_∞ groups. In P. Kielanowski, P. Bieliavsky, A. Odzijewicz, M. Schlichenmaier, & T. Voronov (Eds.), Geometric Methods in Physics - 33rd Workshop, 2014 (pp. 39-47). (Trends in Mathematics; Vol. 71). Springer International Publishing. https://doi.org/10.1007/978-3-319-18212-4_2

R_∞-matrices, triangular l_∞-bialgebras and quantum_∞ groups. / Bashkirov, Denis; Voronov, Alexander A.
Geometric Methods in Physics - 33rd Workshop, 2014. ed. / Piotr Kielanowski; Pierre Bieliavsky; Anatol Odzijewicz; Martin Schlichenmaier; Theodore Voronov. Springer International Publishing, 2015. p. 39-47 (Trends in Mathematics; Vol. 71).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Bashkirov, D & Voronov, AA 2015, R_∞-matrices, triangular l_∞-bialgebras and quantum_∞ groups. in P Kielanowski, P Bieliavsky, A Odzijewicz, M Schlichenmaier & T Voronov (eds), Geometric Methods in Physics - 33rd Workshop, 2014. Trends in Mathematics, vol. 71, Springer International Publishing, pp. 39-47, 33rd Workshop on Geometric Methods in Physics, 2014, Bialowieza, Poland, 6/29/14. https://doi.org/10.1007/978-3-319-18212-4_2

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