Reference : Quantizations of Lie bialgebras, duality involution and oriented graph complexes
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/48728
Quantizations of Lie bialgebras, duality involution and oriented graph complexes
English
Merkoulov (merkulov), Serguei mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Zivkovic, Marko mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Feb-2022
Letters in Mathematical Physics
Kluwer Academic Publishers
DOI 10.1007
s11005-022-01505-6
Yes (verified by ORBilu)
International
0377-9017
1573-0530
Dordrecht
Netherlands
[en] quantization ; Lie bialgebra ; graph complexes
[en] We prove that the action of the Grothendieck-Teichm├╝ller group on the genus completed properad of (homotopy) Lie bialgebras commutes with the reversing directions involution of the latter. We also prove that every universal quantization of Lie bialgebras is homotopy equivalent to the one which commutes with the duality involution exchanging Lie bracket and Lie cobracket. The proofs are based on a new result in the theory of oriented graph complexes (which can be of independent interest) saying that the involution on an oriented graph complex that changes all directions on edges induces the identity map on its cohomology.
http://hdl.handle.net/10993/48728

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