The explicit equivalence between the standard and the logarithmic star product for Lie algebras. II.
This paper etablishes the equivalence between the standard and the logarithmic star product for Lie algebras. Let us recall that two quadratic algebras \(A\) and \(B\) are naturally associated with a Lie algebra, where \(A\) and \(B\) are Koszul algebras and Koszul dual to each other. In this work, the author considers the graded algebras \(A_\hbar\) and \(B_\hbar\) and the logarithmic product obtained via the formality quasi-isomorphism. He proves the equivalence with the standard product. The author gives an explicit proof. The link with the Grotendieck-Teichmüller group is also precised. The result of this paper gives a proof of a particular case of Shoikhet's conjecture. For Part I see [ibid. 350, No. 13--14, 661--664 (2012; Zbl 1271.53075)].
scientific article; zbMATH DE number 6100618
scientific article