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 |
|---|---|
| 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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