A Study on the Centroid of a Class of Solvable Lie Algebras
Author:
Yu Demin1,
Jiang Chan1,
Ma Jiejing1
Affiliation:
1. School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414000, China
Abstract
The centroid of Lie algebra is a basic concept and a necessary tool for studying the structure of Lie algebraic structure. The extended Heisenberg algebra is an important class of solvable Lie algebras. In any Lie algebra, the anti symmetry of Lie operations is an important property of Lie algebra. This article investigates the centroids and structures of 2n+2 dimensional extended Heisenberg algebras, where all invertible elements form a group and all elements form a ring. Then, its main research results are extended to infinite dimensional extended Heisenberg algebras.
Funder
National Natural Science Foundation of China
Hunan Provincial Department of Education
Hunnan Institute of Science and Technology
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference14 articles.
1. The centroid of extended affine and root graded Lie algebras;Benkart;J. Pure Appl. Algebra,2005
2. The centroid of Extended Schrodinger Virasoro Lie Algebras;Chen;J. Huzhou Univ.,2018
3. Centroid of n-Lie superalgebras;Wang;J. Jilin Eng. Norm. Univ.,2006
4. The centroid of a Jordan-Lie algebra;Zhou;J. Nat. Sci. Heilongjiang Univ.,2019
5. Centroid structures of n-Lie algebras;Bai;Linear Algebra Its Appl.,2008