Centralizer and faithful groupoid
type: Item
instance of: scholarly article
title: Centralizer and faithful groupoid
zbMATH Open document ID: 1228.18012
author: Dominique Bourn
published in: Journal of Algebra
publication date: 2011-05-16T00:00:00Z
review text: The author correlates existence and aspect of some properties of centralizers with the conceptual notion of \(\Theta\)-faithful objects in a category. Then, a large choice of examples from standard algebraic situations to topological models is produced. In particular, this allows to assert the existence of centralizers in some of of the new notions of algebras, as Leibniz algebras, introduced by \textit{J.-L. Loday} [Enseign. Math., II. Sér. 39, No.~3--4, 269--293 (1993; Zbl 0806.55009)], associated dialgebras [Dialgebras and related operads, Lect. Notes Math. 1763 (2001; Zbl 0970.00010)] and trialgebras [\textit{J.-L. Loday} and \textit{M. Ronco}, Contemp. Math. 346, 369--398 (2004; Zbl 1065.18007)].
reviewed by: Marek Golasiński
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 17B55
Mathematics Subject Classification ID: 18C99
Mathematics Subject Classification ID: 18D35
Mathematics Subject Classification ID: 20J05
zbMATH DE Number: 5888480
zbMATH Keywords: action representative
zbMATH Keywords: commutator
zbMATH Keywords: centralizer
zbMATH Keywords: internal groupoid
zbMATH Keywords: Mal'cev
zbMATH Keywords: protomodular
zbMATH Keywords: split extension classifier
zbMATH Keywords: Leibniz algebras
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2010.09.030
OpenAlex ID: W1975419865
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DOI: 10.1016/J.JALGEBRA.2010.09.030
description: scientific article; zbMATH DE number 5888480