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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


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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