Braided tensor product and Lie algebra in a braided category.
type: Item
instance of: scholarly article
title: Braided tensor product and Lie algebra in a braided category.
zbMATH Open document ID: 0958.18004
author: A. Haddi
author: S. Hadj Nassar
published in: Beiträge zur Algebra und Geometrie
publication date: 2000-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/231652
full work available at URL: 12.html
review text: The authors study to what extent the notion of a Lie algebra makes sense in an arbitrary additive braided monoidal category \(\mathcal C\). Braided monoidal categories have been introduced by \textit{A. Joyal} and \textit{R. Street} [Adv. Math., Vol. 102, No. 1, 20-78 (1993; Zbl 0817.18007)]. The authors give several equivalent forms of (a braid analog of) Jacobi's identity. They construct for each bialgebra \(B\) of \(\mathcal C\) a primitive part object which is shown to be a Lie algebra if and only if the braiding acts as a symmetry on \(B\). If \(\mathcal C\) is moreover abelian, they construct for each algebra \(A\) of \(\mathcal C\) an object of derivations of \(A\), which is shown to be a Lie algebra.
reviewed by: Clemens Berger
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 17B60
Mathematics Subject Classification ID: 16W10
zbMATH DE Number: 1460288
zbMATH Keywords: braided monoidal category
zbMATH Keywords: Lie algebra
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1460288