The explicit equivalence between the standard and the logarithmic star product for Lie algebras. II.
type: Item
instance of: scholarly article
title: The explicit equivalence between the standard and the logarithmic star product for Lie algebras. II.
zbMATH Open document ID: 1285.53070
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2012-10-31T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 53D17
Mathematics Subject Classification ID: 53D55
zbMATH DE Number: 6100618
zbMATH Keywords: deformation quantization
zbMATH Keywords: logarithmic star product
zbMATH Keywords: Lie algebras
zbMATH Keywords: Shoikhet's conjecture
zbMATH Keywords: Grothendieck-Teichmüller group
author: Carlo A. Rossi
reviewed by: Angela Gammella-Mathieu
MaRDI profile type: Publication
full work available at URL: j.crma.2012.09.003
OpenAlex ID: W2167141158
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DOI: 10.1016/J.CRMA.2012.09.003
description: scientific article; zbMATH DE number 6100618