Friday, February 3, 2012

1109.2290 (Zhuo Chen et al.)

Weak Lie 2-bialgebra    [PDF]

Zhuo Chen, Mathieu Stienon, Ping Xu
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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