This article is cited in 4 papers

RESEARCH ARTICLE

Derivations and relation modules for inverse semigroups

N. D. Gilbert

School of Mathematical and Computer Sciences & the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, U.K.

Abstract: We define the derivation module for a homomorphism of inverse semigroups, generalizing a construction for groups due to Crowell. For a presentation map from a free inverse semigroup, we can then define its relation module as the kernel of a canonical map from the derivation module to the augmentation module. The constructions are analogues of the first steps in the Gruenberg resolution obtained from a group presentation. We give a new proof of the characterization of inverse monoids of cohomological dimension zero, and find a class of examples of inverse semigroups of cohomological dimension one.

Keywords: inverse semigroup, cohomology, derivation, relation module.

MSC: 20M18, 20M50, 18G20

Received: 23.07.2010
Revised: 10.10.2011

Language: English

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