Cohomologies and deformations of O-operators on Lie triple systems-Reference-Cited by-同舟云学术

Cohomologies and deformations of O-operators on Lie triple systems

Published:2023-08-01 Issue:8 Volume:64 Page:
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:

Author:

Chtioui Taoufik¹^ORCID,Hajjaji Atef¹²^ORCID,Mabrouk Sami³^ORCID,Makhlouf Abdenacer²^ORCID

Affiliation:

1. Faculty of Sciences, University of Sfax 1 , B.P. 1171, 3038 Sfax, Tunisia

2. IRIMAS–Département de Mathématiques, University of Haute Alsace 2 , 18, Rue des Frères Lumière, F-68093 Mulhouse, France

3. Faculty of Sciences, University of Gafsa 3 , 2112 Gafsa, Tunisia

Abstract

In this paper, first, we provide a graded Lie algebra whose Maurer–Cartan elements characterize Lie triple system structures. Then, we use it to study cohomology and deformations of O-operators on Lie triple systems by constructing a Lie 3-algebra whose Maurer–Cartan elements are O-operators. Furthermore, we define a cohomology of an O-operator T as the Lie–Yamaguti cohomology of a certain Lie triple system induced by T with coefficients in a suitable representation. Therefore, we consider infinitesimal and formal deformations of O-operators from a cohomological viewpoint. Moreover, we provide relationships between O-operators on Lie algebras and associated Lie triple systems.

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0118911/18076402/081701_1_5.0118911.pdf

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