On split involutive regular BiHom-Lie superalgebras
type: Item
instance of: scholarly article
title: On split involutive regular BiHom-Lie superalgebras
zbMATH Open document ID: 1502.17018
author: Xiaohui Zhang
author: Shengxiang Wang
author: Shuangjian Guo
published in: Open Mathematics
publication date: 2021-11-29T00:00:00Z
review text: This paper under review is concerned with an abstract superalgebraic structure (called \text{split involutive regular BiHom-Lie superalgebras}) that generalizes two kinds of important algebras: split involutive regular Hom-Lie algebras and split regular BiHom-Lie superalgebras. Using some techniques analogous to those appeared in the theory of semisimple Lie algebras and Lie superalgebras, the authors explore several structure theorems of such superalgebras. The authors prove that any ideal of a perfect split involutive regular BiHom-Lie superalgebra that has maximal length and satisfies root-multiplicativity is involutive, as well as characterize simple perfect split involutive regular BiHom-Lie superalgebras with maximal length and root-multiplicativity by an equivalence relation. Finally, the authors prove that any perfect split involutive regular BiHom-Lie superalgebra with maximal length and root-multiplicativity is a direct sum of simple involutive ideals, where each of these ideals has all its roots connected.
reviewed by: Yin Chen
Mathematics Subject Classification ID: 17B61
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 17B65
zbMATH DE Number: 7435370
zbMATH Keywords: involutive
zbMATH Keywords: BiHom-Lie superalgebra
zbMATH Keywords: root space
zbMATH Keywords: structure theory
MaRDI profile type: Publication
full work available at URL: math-2020-0144
OpenAlex ID: W3033728512
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DOI: 10.1515/MATH-2020-0144
description: scientific article; zbMATH DE number 7435370