2,471 research outputs found
Unary FA-presentable semigroups
Automatic presentations, also called FA-presentations, were introduced to extend nite model theory to innite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has been the classication of those structures of some species that admit automatic presentations. Whilst some successes have been obtained, this appears to be a dicult problem in general. A restricted problem, also of signicant interest, is to ask this question for unary automatic presentations: auto-matic presentations over a one-letter alphabet. This paper studies unary FA-presentable semigroups. We prove the following: Every unary FA-presentable structure admits an injective unary automatic presentation where the language of representatives consists of every word over a one-letter alphabet. Unary FA-presentable semigroups are locally nite, but non-nitely generated unary FA-presentable semigroups may be innite. Every unary FA-presentable semigroup satises some Burnside identity.We describe the Green's relations in unary FA-presentable semigroups. We investigate the relationship between the class of unary FA-presentable semigroups and various semigroup constructions. A classication is given of the unary FA-presentable completely simple semigroups.PostprintPeer reviewe
C*-Algebras of algebraic dynamical systems and right LCM semigroups
We introduce algebraic dynamical systems, which consist of an action of a
right LCM semigroup by injective endomorphisms of a group. To each algebraic
dynamical system we associate a C*-algebra and describe it as a semigroup
C*-algebra. As part of our analysis of these C*-algebras we prove results for
right LCM semigroups. More precisely we discuss functoriality of the full
semigroup C*-algebra and compute its K-theory for a large class of semigroups.
We introduce the notion of a Nica-Toeplitz algebra of a product system over a
right LCM semigroup, and show that it provides a useful alternative to study
algebraic dynamical systems.Comment: 28 pages, to appear in Indiana Univ. Math.
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