Cohomology and extensions of ordered groupoids

Bernard Oduoku Bainson; N. D. Gilbert

doi:10.1142/S0219498822501778

Cohomology and extensions of ordered groupoids

Bernard Oduoku Bainson
, N. D. Gilbert

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Abstract

We adapt and generalize results of Loganathan on the cohomology of inverse semigroups to the cohomology of ordered groupoids. We then derive a five-term exact sequence in cohomology from an extension of ordered groupoids, and show that this sequence leads to a classification of extensions by a second cohomology group. Our methods use structural ideas in cohomology as far as possible, rather than computation with cocycles.

Original language	English
Article number	2250177
Journal	Journal of Algebra and its Applications
Volume	21
Issue number	9
Early online date	3 Jun 2021
DOIs	https://doi.org/10.1142/S0219498822501778
Publication status	Published - Sept 2022

Keywords

Cohomology
Extension
Groupoid
Module

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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AB - We adapt and generalize results of Loganathan on the cohomology of inverse semigroups to the cohomology of ordered groupoids. We then derive a five-term exact sequence in cohomology from an extension of ordered groupoids, and show that this sequence leads to a classification of extensions by a second cohomology group. Our methods use structural ideas in cohomology as far as possible, rather than computation with cocycles.

KW - Cohomology

KW - Extension

KW - Groupoid

KW - Module

UR - https://www.scopus.com/pages/publications/85107776397

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DO - 10.1142/S0219498822501778

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Cohomology and extensions of ordered groupoids

Abstract

Keywords

ASJC Scopus subject areas

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