ON THE KROHN–RHODES COMPLEXITY OF SEMIGROUPS OF UPPER TRIANGULAR MATRICES-Reference-Cited by-同舟云学术

ON THE KROHN–RHODES COMPLEXITY OF SEMIGROUPS OF UPPER TRIANGULAR MATRICES

Published:2007-02 Issue:01 Volume:17 Page:187-201
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

KAMBITES MARK¹

Affiliation:

1. School of Mathematics, University of Manchester, Sackville Street, Manchester M60 1QD, England

Abstract

We consider the Krohn–Rhodes complexity of certain semigroups of upper triangular matrices over finite fields. We show that for any n > 1 and finite field k, the semigroups of all n × n upper triangular matrices over k and of all n × n unitriangular matrices over k have complexity n - 1. A consequence is that the complexity c > 1 of a finite semigroup places a lower bound of c + 1 on the dimension of any faithful triangular representation of that semigroup over a finite field.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196707003548

Reference8 articles.

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