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Representations of inverse semigroups in complete atomistic inverse meet-semigroups

Citation

FitzGerald, DG, Representations of inverse semigroups in complete atomistic inverse meet-semigroups, Semigroup Forum, 101 pp. 87-101. ISSN 0037-1912 (2020) [Refereed Article]


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Copyright 2020 Springer Nature Switzerland AG

DOI: doi:10.1007/s00233-020-10091-9

Abstract

As an appropriate generalisation of the features of the classical (Schein) theory of representations of inverse semigroups in I 𝑋, a theory of representations of inverse semigroups by homomorphisms into complete atomistic inverse ∧-semigroups is developed. This class of inverse ∧-semigroups, otherwise known as inverse algebras, includes partial automorphism monoids of entities such as graphs, vector spaces and modules. A workable theory of decompositions is reached; however complete distributivity is required for results approaching those of the classical case.

Item Details

Item Type:Refereed Article
Keywords:Inverse semigroups; Representation of semigroups; Inverse meet semigroups; Partial automorphism monoids
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Group theory and generalisations
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:FitzGerald, DG (Dr Des FitzGerald)
ID Code:140879
Year Published:2020
Deposited By:Mathematics
Deposited On:2020-09-14
Last Modified:2020-10-29
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