TY - JOUR
T1 - Weak Lie 2-bialgebras
AU - Chen, Zhuo
AU - Stiénon, Mathieu
AU - Xu, Ping
N1 - Funding Information:
Research partially supported by NSF grants DMS-0605725 , DMS-0801129 , DMS-1101827 and NSFC grant 11001146 .
PY - 2013/6
Y1 - 2013/6
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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U2 - 10.1016/j.geomphys.2013.01.006
DO - 10.1016/j.geomphys.2013.01.006
M3 - Article
AN - SCOPUS:84874802776
SN - 0393-0440
VL - 68
SP - 59
EP - 68
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
ER -