Representation theory of comtrans algebras
type: Item
instance of: scholarly article
title: Representation theory of comtrans algebras
zbMATH Open document ID: 0758.17001
DOI: 10.1016/0022-4049(92)90077-S
author: Xiarong Shen
author: J. D. H. Smith
published in: Journal of Pure and Applied Algebra
publication date: 1993-01-16T00:00:00Z
review text: A comtrans algebra \(E\) over a commutative ring \(R\) with 1 is an \(R\)- module \(E\) equipped with two trilinear operations \([ , , ]\) and \(\langle , ,\rangle\) from \(E^ 3\) to \(E\) such that \([x,x,z]=0\), \(\langle x,y,z\rangle+\langle y,z,x\rangle+\langle z,x,y\rangle=0\) and \([x,y,x]=\langle x,y,z\rangle\) for all \(x,y,z\in E\). These algebras first appeared from a problem in differential geometry [\textit{C. Scheiderer}, Gewebegeometrie, Tagungsbericht 27, Mathematisches Forschungsinstitut Oberwolfach (1984)]. This paper considers representations of these algebras by showing that they are equivalent to the representations of an associative universal enveloping algebra. The structure of the universal algebra of \(E\) is that of the tensor algebra of \(V=(E\wedge E)\oplus(E\otimes E)\oplus(E\otimes E)\).
Mathematics Subject Classification ID: 17A30
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 53A60
Mathematics Subject Classification ID: 17B60
zbMATH DE Number: 89581
zbMATH Keywords: commutator
zbMATH Keywords: translator
zbMATH Keywords: comtrans algebra
zbMATH Keywords: trilinear operations
zbMATH Keywords: representations
zbMATH Keywords: universal enveloping algebra
reviewed by: Ernest L. Stitzinger
MaRDI profile type: Publication
cites work: Q4039680
cites work: Q3994471
cites work: Q5682456
cites work: Homotopical algebra
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description: scientific article; zbMATH DE number 89581