\(L_{\infty}\) algebra representations
type: Item
instance of: scholarly article
title: \(L_{\infty}\) algebra representations
zbMATH Open document ID: 1067.17013
DOI: 10.1023/B:APCS.0000013809.71153.30
author: Tom Lada
published in: Applied Categorical Structures
publication date: 2004-05-27T00:00:00Z
review text: An \(L_\infty\)-algebra on a differential graded vector space \(L\) may be described by a coderivation \(D\) of degree \(+1\) on the cofree commutative coalgebra \(\wedge^* sL\), with \(D^2= 0\). A notion of left module over \(L_\infty\) algebras appeared in [\textit{T. Lada} and \textit{M. Markl}, Strongly homotopy Lie algebras, Commun. Algebra, 23, No. 6, 2147--2161 (1995; Zbl 0999.17019)]. In the paper under review, the author proves that, if \(L\) is an \(L_\infty\)-algebra and \(M\) a left \(L\)-module, then \(L\oplus M\) has an \(L_\infty\)-algebra structure. An explicit description in terms of a collection of linear maps \(j_k: \bigotimes^k(L\oplus M)\to L\oplus M\) is given. This is the homotopy theoretic version of a classical similar result in the setting of modules over Lie algebras.
Mathematics Subject Classification ID: 17B99
Mathematics Subject Classification ID: 18G99
Mathematics Subject Classification ID: 55U99
zbMATH DE Number: 2069038
zbMATH Keywords: \(L_\infty\) algebra
zbMATH Keywords: \(L_\infty\) module
reviewed by: Daniel Tanré
MaRDI profile type: Publication
Recommended article: Q4298404
Recommended article: \(L_{\infty}\)-algebra actions
Recommended article: Q6161806
Recommended article: Q5872096
Recommended article: Q3377696
Recommended article: Representations of Derived 𝐴-infinity Algebras
Recommended article: Infinite dimensional representations of finite dimensional algebras and amenability
Recommended article: Integrating -algebras
Recommended article: Representations of Dirichlet operator algebras
Recommended article: Q4533148
description: scientific article; zbMATH DE number 2069038