Weak Lie 2-bialgebra

Details Weak Lie 2-bialgebra Weak Lie 2-bialgebra

2011-09-11

arxiv.org/abs/1109.2290v2

Physics

Mathematical Physics

10 pages, LaTeX; typos added, references modified

Scientific paper

We introduce the notion of weak Lie 2-bialgebra. Roughly, a weak Lie
2-bialgebra is a pair of compatible 2-term $L_\infty$-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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