All Title Author
Keywords Abstract

Publish in OALib Journal
ISSN: 2333-9721
APC: Only $99

ViewsDownloads

Relative Articles

More...

Root Systems Lie Algebras

DOI: 10.4236/alamt.2023.131001, PP. 1-20

Keywords: Lie Algebras, Root Systems, Ways Chambers, Dynkin Diagrams

Full-Text   Cite this paper   Add to My Lib

Abstract:

A root system is any collection of vectors that has properties that satisfy the roots of a semi simple Lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclidean vector space that possesses some remarkable symmetries and completely defines the Lie algebra of g. The purpose of this paper is to show the essentiality of the root system on the Lie algebra. In addition, the paper will mention the connection between the root system and Ways chambers. In addition, we will show Dynkin diagrams, which are an integral part of the root system.

References

[1]  Roberts, B. (2018-2019) Lie Algebras. University of Idaho, Moscow.
https://www.webpages.uidaho.edu/~brooksr/liealgebraclass.pdf
[2]  Gonzalez, F.B. (2007) Lie Algebras.
https://fgonzale.pages.tufts.edu/lie.algebras.book.pdf
[3]  Hasic, A. (2021) Introduction to Lie Algebras and Their Representations. Advances in Linear Algebra & Matrix Theory, 11, 67-91.
Introduction to Lie Algebras and Their Representations (scirp.org)
https://doi.org/10.4236/alamt.2021.113006
[4]  Onishchik, A.L. and Vinberg, E.B. (Eds.) (1990) Lie Groups and Lie Algebras III. Structure of Lie Groups and Lie Algebras. VINITI, Moscow.
https://books.google.me/books?id=l8nJCNiIQAAC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false
[5]  Wikipedia (2023) Root System.
https://en.wikipedia.org/wiki/Root_system

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133