Generalized Lie-Cartan pairs
type: Item
instance of: scholarly article
title: Generalized Lie-Cartan pairs
zbMATH Open document ID: 0741.17014
DOI: 10.1016/0034-4877(89)90020-7
author: Władysław Marcinek
published in: Reports on Mathematical Physics
publication date: 1992-06-26T00:00:00Z
review text: \textit{D. Kastler} and \textit{R. Stora} [J. Geom. Phys. 2, No. 3, 1-31 (1985; Zbl 0593.17009)] defined the Lie-Cartan pairs \((L,A)\) of a Lie algebra \(L\) and a commutative algebra \(A\). \textit{A. Jadczyk} and \textit{D. Kastler} [Rep. Math. Phys. 25, No. 1, 1-51 (1988; Zbl 0656.17014)] generalized the concept of Lie-Cartan pairs to the \(\mathbb{Z}_ 2\)-graded case. The author generalizes it to the \(\Gamma\)-graded case, where \(\Gamma\) is a \(p\)-group for \(p=2\). The author shows that classical operators of differential geometry such as the exterior derivative, covariant derivative, the inner product, Lie derivative can be extended to the \(\Gamma\)-graded case.
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17A70
zbMATH DE Number: 21546
zbMATH Keywords: \(\Gamma\)-graded algebras
zbMATH Keywords: \(\Gamma\)-graded modules
zbMATH Keywords: generalized tensor product
zbMATH Keywords: generalized exterior product
zbMATH Keywords: generalized Lie-Cartan pairs
zbMATH Keywords: generalized connection
zbMATH Keywords: generalized curvature tensor
MaRDI profile type: Publication
full work available at URL: 0034-4877(89)90020-7
OpenAlex ID: W2079265115
cites work: Lie-Cartan pairs
cites work: Generalized Lie algebras
cites work: Lie groups and Lie algebras with generalized supersymmetric parameters
description: scientific article; zbMATH DE number 21546