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Epsilon-Strongly Groupoid-Graded Rings, The Picard Inverse Category And Cohomology
University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.ORCID iD: 0000-0001-6594-7041
Blekinge Inst Technol, Dept Math & Nat Sci, SE-37179 Karlskrona, Sweden.
Univ Ind Santander, Escuela Matemat, Carrera 27 Calle 9, Bucaramanga, Colombia.
2020 (English)In: Glasgow Mathematical Journal, ISSN 0017-0895, E-ISSN 1469-509X, Vol. 62, no 1, p. 233-259Article in journal (Refereed) Published
Abstract [en]

We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call, generalized epsilon-crossed products and show that these coincide with the class of epsilon-strongly groupoid-graded rings. We then use generalized epsilon-crossed groupoid products to obtain a generalization, from the group-graded situation to the groupoid-graded case, of the bijection from a certain second cohomology group, defined by the grading and the functor from the groupoid in question to the Picard inverse category, to the collection of equivalence classes of rings epsilon-strongly graded by the groupoid.

Place, publisher, year, edition, pages
2020. Vol. 62, no 1, p. 233-259
Keywords [en]
Primary: 16W50; Secondary: 16E99; 16D99; 14C22
National Category
Discrete Mathematics
Research subject
ENGINEERING, Mathematics
Identifiers
URN: urn:nbn:se:hv:diva-14794DOI: 10.1017/S0017089519000065ISI: 000500321900015Scopus ID: 2-s2.0-85076344944OAI: oai:DiVA.org:hv-14794DiVA, id: diva2:1395686
Available from: 2020-02-24 Created: 2020-02-24 Last updated: 2020-03-10Bibliographically approved

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