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EPSILON-STRONGLY GROUPOID-GRADED RINGS, THE PICARD INVERSE CATEGORY AND COHOMOLOGY
Univ West, SWE.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.ORCID iD: 0000-0001-8095-0820
Univ Ind Santander, COL.
2020 (English)In: Glasgow Mathematical Journal, ISSN 0017-0895, E-ISSN 1469-509X, Vol. 62, no 1, p. 233-259, article id PII S0017089519000065Article 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
CAMBRIDGE UNIV PRESS , 2020. Vol. 62, no 1, p. 233-259, article id PII S0017089519000065
Keywords [en]
Primary: 16W50, Secondary: 16E99, 16D99, 14C22
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:bth-19023DOI: 10.1017/S0017089519000065ISI: 000500321900015OAI: oai:DiVA.org:bth-19023DiVA, id: diva2:1380080
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open access

Available from: 2019-12-18 Created: 2019-12-18 Last updated: 2019-12-27Bibliographically approved

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Öinert, Johan

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