R-matrices, triangular l-bialgebras and quantum groups

Denis Bashkirov, Alexander A Voronov

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 languageEnglish (US)
Title of host publicationGeometric Methods in Physics - 33rd Workshop, 2014
EditorsPiotr Kielanowski, Pierre Bieliavsky, Anatol Odzijewicz, Martin Schlichenmaier, Theodore Voronov
PublisherSpringer International Publishing
Number of pages9
ISBN (Print)9783319182117
StatePublished - 2015
Event33rd Workshop on Geometric Methods in Physics, 2014 - Bialowieza, Poland
Duration: Jun 29 2014Jul 5 2014

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X


Other33rd Workshop on Geometric Methods in Physics, 2014

Bibliographical note

Publisher Copyright:
© 2015 Springer International Publishing Switzerland.


  • 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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