alexa Abstract | Classification of Maximal Subalgebras and Corresponding Reductive Pairs of Lie Algebra of All 2 × 2 Real Matrices
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
Open Access

OMICS International organises 3000+ Global Conferenceseries Events every year across USA, Europe & Asia with support from 1000 more scientific Societies and Publishes 700+ Open Access Journals which contains over 50000 eminent personalities, reputed scientists as editorial board members.

Open Access Journals gaining more Readers and Citations

700 Journals and 15,000,000 Readers Each Journal is getting 25,000+ Readers

This Readership is 10 times more when compared to other Subscription Journals (Source: Google Analytics)

Research Article Open Access


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.

To read the full article Peer-reviewed Article PDF image | Peer-reviewed Full Article image

Author(s): Shtukar U


Lie algebra, Subalgebras, Reductive pairs, Algebra, Combinatorics, Deformations Theory, Geometry, Harmonic Analysis, Homological Algebra, Homotopical Algebra, Latin Squares, Lie Theory, Lie Triple Systems, Loop Algebra, Operad Theory, Quantum Group, Quasi-Group, Representation theory, Super Algebras, Lie Superalgebra, Symmetric Spaces, Topologies, Lie Algebra

Share This Page

Additional Info

Loading Please wait..
Peer Reviewed Journals
Make the best use of Scientific Research and information from our 700 + peer reviewed, Open Access Journals
International Conferences 2017-18
Meet Inspiring Speakers and Experts at our 3000+ Global Annual Meetings

Contact Us

© 2008-2017 OMICS International - Open Access Publisher. Best viewed in Mozilla Firefox | Google Chrome | Above IE 7.0 version