15,020 research outputs found
A proof of Zhil'tsov's theorem on decidability of equational theory of epigroups
Epigroups are semigroups equipped with an additional unary operation called
pseudoinversion. Each finite semigroup can be considered as epigroup. We prove
the following theorem announced by Zhil'tsov in 2000: the equational theory of
the class of all epigroups coincides with the equational theory of the class of
all finite epigroups and is decidable. We show that the theory is not finitely
based but provide a transparent infinite basis for it.Comment: 32 page
Dimension Representations of the Braid Group on Strings
In 1996 E. Formanek classified all the irreducible complex representations of
of dimension at most where is the Artin braid group on
strings. In this paper we extend this classification to the representations of
dimension for . We prove that all such representations are
equivalent to a tensor product of a one-dimensional representation and a
specialization of a certain one-parameter family of dimensional
representations, that was first discovered in 1996 by Tong, Yang, and Ma. We
use our classification of irreducible complex representations of corank two, in
the preprint math.GR/0003047.Comment: 6 page
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