Bibliographic Details
| Title: |
Counting gradings on Lie algebras of block-triangular matrices. |
| Authors: |
Diniz, Diogo1 (AUTHOR) diogo@mat.ufcg.edu.br, Borges, Alex Ramos2 (AUTHOR) alex.borges@upe.br, Fonsêca, Eduardo1 (AUTHOR) eduardo@mat.ufcg.edu.br |
| Source: |
Linear Algebra & its Applications. Dec2024, Vol. 703, p504-527. 24p. |
| Subjects: |
Lie algebras, Isomorphism (Mathematics), Matrices (Mathematics), Finite groups, Number theory, Abelian groups |
| Abstract: |
We study the number of isomorphism classes of gradings on Lie algebras of block-triangular matrices. Let G be a finite abelian group, for m ∈ N s we determine the number E (−) (G , m) of isomorphism classes of elementary G -gradings on the Lie algebra U T (m) (−) of block-triangular matrices over an algebraically closed field of characteristic zero. We study the asymptotic growth of E (−) (G , m) and as a consequence prove that the E (−) (G , ⋅) determines G up to isomorphism. We also study the asymptotic growth of the number N (−) (G , m) of isomorphism classes of G -gradings on U T (m) (−) and prove that N (−) (G , m)) ∼ | G | E (−) (G , m). [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
