Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902985 | Discrete Mathematics | 2018 | 10 Pages |
Abstract
It is known that each positive definite quasi-Cartan matrix A is Z-equivalent to a Cartan matrix AÎ called Dynkin type of A, the matrix AÎ is uniquely determined up to conjugation by permutation matrices. However, in most of the cases, it is not possible to determine the Dynkin type of a given connected quasi-Cartan matrix by simple inspection. In this paper, we give a graph theoretical characterization of non-symmetric connected quasi-Cartan matrices. For this purpose, a special assemblage of blocks is introduced. This result complements the approach proposed by Barot (1999, 2001), for An, Dn and Em with m=6,7,8.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Claudia Pérez, Daniel Rivera,