alexa Classification of Maximal Subalgebras and Corresponding Reductive Pairs of Lie Algebra of All 2 and#215; 2 Real Matrices | OMICS International | Abstract
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article

Classification of Maximal Subalgebras and Corresponding Reductive Pairs of Lie Algebra of All 2 × 2 Real Matrices

Shtukar U*

Math/Physics Department, North Carolina Central University, Durham, USA

*Corresponding Author:
Shtukar U
Associate Professor, Math/Physics Department
North Carolina Central University
1801 Fayetteville Street, Durham, NC 27707, USA
Tel: 919-597-0375
E-mail: [email protected]

Received date: February 19, 2017; Accepted date: April 10, 2017; Published date: April 17, 2017

Citation: Shtukar U (2017) Classification of Maximal Subalgebras and Corresponding Reductive Pairs of Lie Algebra of All 2 × 2 Real Matrices. J Generalized Lie Theory Appl 11: 263. doi: 10.4172/1736-4337.1000263

Copyright: © 2017 Shtukar U. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abstract

The purpose of the article is to describe all 3-dimensional subalgebras and all corresponding reductive pairs of Lie algebra of all 2 × 2 real matrices. This Lie algebra is 4-dimensional as a vector space, it’s not simple, and it’s not solvable. The evaluation procedure utilizes the canonical bases for subspaces that were introduced. In Part I of this article, all 3-dimensional subalgebras of the given Lie algebra g are classified. All reductive pairs {h, m} with 3-dimensional subalgebras h are found in Part II. Surprisingly, there is only one reductive pair {h, m} with special 3-dimensional subalgebra h and 1-dimensional complement m. Finally, all reductive pairs {h, m} with 1-dimensional subalgebras h of algebra g are classified in Part III of the article.

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