Structure of centralizer matrix algebras
| Autor: | Changchang Xi, Jinbi Zhang |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Ring (mathematics) Algebra and Number Theory 010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences Matrix ring Centralizer and normalizer Integral domain law.invention Combinatorics Matrix (mathematics) Invertible matrix law Discrete Mathematics and Combinatorics Cellular algebra Geometry and Topology 0101 mathematics Algebraically closed field Mathematics |
| Zdroj: | Linear Algebra and its Applications. 622:215-249 |
| ISSN: | 0024-3795 |
| Popis: | Given an n × n matrix c over a unitary ring R, the centralizer of c in the full n × n matrix ring M n ( R ) is called a principal centralizer matrix ring, denoted by S n ( c , R ) . We investigate its structure and prove: (1) If c is an invertible matrix with a c-free point, or if R has no zero-divisors and c is a Jordan-similar matrix with all eigenvalues in the center of R, then M n ( R ) is a separable Frobenius extension of S n ( c , R ) in the sense of Kasch. (2) If R is an integral domain and c is a Jordan-similar matrix, then S n ( c , R ) is a cellular R-algebra in the sense of Graham and Lehrer. In particular, if R is an algebraically closed field and c is an arbitrary matrix in M n ( R ) , then S n ( c , R ) is always a cellular algebra, and the extension S n ( c , R ) ⊆ M n ( R ) is always a separable Frobenius extension. |
| Databáze: | OpenAIRE |
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