On the Krohn-Rhodes complexity of semigroups of upper triangular matrices

Kambites, Mark (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

[img] PDF

Download (152kB)
Official URL: http://www.worldscinet.com/cgi-bin/details.cgi?id=...


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 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User: Ms Lucy van Russelt
Date Deposited: 27 Nov 2007
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/964

Actions (login required)

View Item View Item