4 Citations (Scopus)

Abstract

We introduce the notion of weak Lie 2-bialgebra. Roughly, a weak Lie 2-bialgebra is a pair of compatible 2-term L-algebra structures on a vector space and its dual. The compatibility condition is described in terms of the big bracket. We prove that (strict) Lie 2-bialgebras are in one-one correspondence with crossed modules of Lie bialgebras.

Original languageEnglish (US)
Pages (from-to)59-68
Number of pages10
JournalJournal of Geometry and Physics
Volume68
DOIs
StatePublished - Jun 1 2013

Fingerprint

Bialgebra
vector spaces
brackets
compatibility
algebra
modules
Crossed Module
Lie Bialgebra
Compatibility Conditions
Brackets
One to one correspondence
Vector space
Algebra
Term

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

Cite this

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title = "Weak Lie 2-bialgebras",
abstract = "We introduce the notion of weak Lie 2-bialgebra. Roughly, a weak Lie 2-bialgebra is a pair of compatible 2-term L∞-algebra structures on a vector space and its dual. The compatibility condition is described in terms of the big bracket. We prove that (strict) Lie 2-bialgebras are in one-one correspondence with crossed modules of Lie bialgebras.",
author = "Zhuo Chen and Stienon, {Mathieu Philippe} and Ping Xu",
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Weak Lie 2-bialgebras. / Chen, Zhuo; Stienon, Mathieu Philippe; Xu, Ping.

In: Journal of Geometry and Physics, Vol. 68, 01.06.2013, p. 59-68.

Research output: Contribution to journalArticle

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AU - Chen, Zhuo

AU - Stienon, Mathieu Philippe

AU - Xu, Ping

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N2 - We introduce the notion of weak Lie 2-bialgebra. Roughly, a weak Lie 2-bialgebra is a pair of compatible 2-term L∞-algebra structures on a vector space and its dual. The compatibility condition is described in terms of the big bracket. We prove that (strict) Lie 2-bialgebras are in one-one correspondence with crossed modules of Lie bialgebras.

AB - We introduce the notion of weak Lie 2-bialgebra. Roughly, a weak Lie 2-bialgebra is a pair of compatible 2-term L∞-algebra structures on a vector space and its dual. The compatibility condition is described in terms of the big bracket. We prove that (strict) Lie 2-bialgebras are in one-one correspondence with crossed modules of Lie bialgebras.

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