Title :
The Bilinear Form of a Class of Lie Algebra
Author :
Yanyan, Zhang ; Jianbo, Liu
Author_Institution :
Dept. of Electron. Inf., Northeastern Univ. at Qinhuangdao, Qinhuangdao, China
Abstract :
In this article, a class of Lie algebra G(A) are introduced, which associated to generalized Cartan matrices A and have much simpler structure than Kac-Moody algebras, We prove that G(A) has a non-degenerate invariant symmetric bilinear form if and only if A is symmetrizable.
Keywords :
Lie algebras; matrix algebra; Kac Moody algebra; Lie algebra; generalized Cartan matrix; nondegenerate invariant symmetric bilinear form; Cryptography; Electronic mail; Knowledge engineering; Matrices; Presses; Symmetric matrices; Kac-Moody algebra; Lie algebra; bilinear form;
Conference_Titel :
Cryptography and Network Security, Data Mining and Knowledge Discovery, E-Commerce & Its Applications and Embedded Systems (CDEE), 2010 First ACIS International Symposium on
Conference_Location :
Qinhuangdao
Print_ISBN :
978-1-4244-9595-5
DOI :
10.1109/CDEE.2010.30
