Regular Hom–Lie structures on strictly upper triangular matrix Lie algebras
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Published:2021-01-20
Issue:
Volume:
Page:2250081
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ISSN:0219-4988
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Container-title:Journal of Algebra and Its Applications
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language:en
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Short-container-title:J. Algebra Appl.
Author:
Chen Zhengxin1,
Yu Yalong1
Affiliation:
1. College of Mathematics and Informatics Science & FJKLMAA, Fujian Normal University, Fuzhou 350007, P. R. China
Abstract
A Hom-structure on a Lie algebra [Formula: see text] is a linear map [Formula: see text] which satisfies the Hom–Jacobi identity [Formula: see text] for all [Formula: see text]. A Hom-structure is called regular if [Formula: see text] is also a Lie algebra isomorphism. Let [Formula: see text] be the Lie algebra consisting of all strictly upper triangular [Formula: see text] matrices over a field [Formula: see text]. In this paper, we prove that if [Formula: see text], any regular Hom-structure [Formula: see text] on [Formula: see text] is a product of a special inner automorphism, an extremal inner automorphism and a central automorphism of [Formula: see text]. As its application, the set of all regular Hom-structures on [Formula: see text] forms a normal subgroup of the automorphism group of [Formula: see text].
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
1 articles.
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1. Regular Hom-Lie structures on incidence algebras;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2023-05-20