Derivations and relation modules for inverse semigroups

N. D. Gilbert

Algebra and discrete mathematics, Tome 12 (2011) no. 1, pp. 1-19.

Résumé

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.

Détail

Keywords: inverse semigroup, cohomology, derivation
Mots-clés : relation module.

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