## 2007.214: On the Krohn-Rhodes complexity of semigroups of upper triangular matrices

2007.214:
Mark Kambites
(2007)
*On the Krohn-Rhodes complexity of semigroups of upper triangular matrices.*
International Journal of Algebra and Computation, 17 (1).
pp. 187-201.
ISSN 0218-1967

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DOI: 10.1142/S0218196707003548

## 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.

Item Type: | Article |
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Uncontrolled Keywords: | Finite semigroups upper triangular matrices Krohn–Rhodes complexity 20M99 (AMSC) |

Subjects: | MSC 2000 > 20 Group theory and generalizations |

MIMS number: | 2007.214 |

Deposited By: | Mrs Louise Healey |

Deposited On: | 27 November 2007 |

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