Article
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Generalized Reynolds Operators on Hom-Lie Triple Systems
Version 1
: Received: 31 December 2023 / Approved: 2 January 2024 / Online: 2 January 2024 (10:00:34 CET)
A peer-reviewed article of this Preprint also exists.
Xiao, Y.; Teng, W.; Long, F. Generalized Reynolds Operators on Hom-Lie Triple Systems. Symmetry 2024, 16, 262, doi:10.3390/sym16030262. Xiao, Y.; Teng, W.; Long, F. Generalized Reynolds Operators on Hom-Lie Triple Systems. Symmetry 2024, 16, 262, doi:10.3390/sym16030262.
Abstract
Uchino first initiated the study of generalized Reynolds operators on associative algebras.
Recently, related research has become a hot topic. In this paper, we first introduce the notion of generalized Reynolds operators on Hom-Lie triple systems associated to a representation and a 3-cocycle.
Then, we develop cohomology of generalized Reynolds operators on Hom-Lie triple systems with coefficients in a suitable representation. As applications, we use the first cohomology group to classify linear deformations and we study the obstruction class of an extendable
order $n$ deformation. Finally, we introduce and investigate Hom-NS-Lie triple system as the underlying
structure of generalized Reynolds operators on Hom-Lie triple systems.
Keywords
Hom-Lie triple system; generalized Reynolds operator; cohomology; deformation; Hom-NS-Lie triple system
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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