The algebra generated by nilpotent elements in a matrix centralizer | Zendy

Ralph John de la Cruz | Zendy; Eloise Misa | Zendy

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The algebra generated by nilpotent elements in a matrix centralizer

Author(s) -

Ralph John de la Cruz,

Eloise Misa

Publication year - 2021

Publication title -

electronic journal of linear algebra

Language(s) - English

Resource type - Journals

eISSN - 1537-9582

pISSN - 1081-3810

DOI - 10.13001/ela.2022.6503

Subject(s) - centralizer and normalizer , subalgebra , mathematics , nilpotent , nilpotent matrix , pure mathematics , cartan subalgebra , square matrix , matrix (chemical analysis) , set (abstract data type) , algebra over a field , discrete mathematics , combinatorics , eigenvalues and eigenvectors , symmetric matrix , affine lie algebra , computer science , physics , chemistry , current algebra , chromatography , quantum mechanics , programming language

For an arbitrary square matrix $S$, denote by $C(S)$ the centralizer of $S$, and by $C(S)_N$ the set of all nilpotent elements in $C(S)$. In this paper, we use the Weyr canonical form to study the subalgebra of $C(S)$ generated by $C(S)_N$. We determine conditions on $S$ such that $C(S)_N$ is a subalgebra of $C(S)$. We also determine conditions on $S$ such that the subalgebra generated by $C(S)_N$ is $C(S).$

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