Abstract
In our previous work (math/0008128), we studied the set Quant(K) of all universal quantization functors of Lie bialgebras over a field K of characteristic zero, compatible with the operations of taking duals and doubles. We showed that Quant(K) is canonically isomorphic to a product G0(K)×ш(K), where G0(K) is a universal group and ш(K) is a quotient set of a set B(K) of families of Lie polynomials by the action of a group G(K). We prove here that G0(K) is equal to the multiplicative group 1+ℏK[[ℏ]]. So Quant(K) is “as close as it can be” to ш(K). We also prove that the only universal derivations of Lie bialgebras are multiples of the composition of the bracket with the cobracket. Finally, we prove that the stabilizer of any element of B(K) is reduced to the 1-parameter subgroup generated by the corresponding “square of the antipode.”
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
