Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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