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 languageEnglish
Number of pages23
JournalJournal of Algebra and its Applications
Early online date3 Jun 2021
DOIs
Publication statusE-pub ahead of print - 3 Jun 2021

Keywords

  • Groupoid
  • Modules
  • cohomology
  • EXTENSION

ASJC Scopus subject areas

  • Mathematics(all)

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