Corepresentations of Munn matrix algebras

Authors

DOI:

https://doi.org/10.17721/1812-5409.2022/3.5

Keywords:

corepresentation, generators and defining relations, noncommutative polynomial, Mann algebra, Rees semigroup, regular sandwich matrix

Abstract

Let A be an algebra over a field K, m and n natural numbers and P = (pji) a fixed n x m matrix over A. The K-vector space of all m x n matrices over the algebra A can be made into an algebra with respect to the following operation (o): B o C = BPC. This algebra is called the Munn matrix algebra over A with sandwich matrix P. The algebras of such type arose as generalizations of semigroup algebras of Rees matrix semigroups which in turn are closely related to simple semigroups.

This article describes the generators and defining relations of Mann matrix algebras with a regular sandwich matrix.

Pages of the article in the issue: 42 - 44

Language of the article: English

References

CLIFFORD A. H., PRESTON G. B. (1961) The algebraic theory of semigroups. Vol. 1, American Mathematical Society, Providence, RI, XV+, 254 pp.

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Published

2022-12-09

How to Cite

Bondarenko, V. M. (2022). Corepresentations of Munn matrix algebras. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, (3), 42–44. https://doi.org/10.17721/1812-5409.2022/3.5

Issue

No. 3 (2022)

Section

Algebra, Geometry and Probability Theory

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Copyright (c) 2022 V. M. Bondarenko

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