Geodesic
Strongly groupoid graded rings and cohomology
Patrik Lundström 1
1 Department of Technology, Mathematics and Computer Science University West Gärdhemsvägen 4 Box 957 461 29, Trollhättan, Sweden
Colloquium Mathematicum, Tome 106 (2006) no. 1, pp. 1-13 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We interpret the collection of invertible bimodules as a groupoid and call it the Picard groupoid. We use this groupoid to generalize the classical construction of crossed products to what we call groupoid crossed products, and show that these coincide with the class of strongly groupoid graded rings. We then use groupoid crossed products to obtain a generalization from the group graded situation to the groupoid graded case of the bijection from a second cohomology group, defined by the grading and the functor from the groupoid in question to the Picard groupoid, to the collection of equivalence classes of rings strongly graded by the groupoid.
DOI : 10.4064/cm106-1-1
Keywords: interpret collection invertible bimodules groupoid call picard groupoid groupoid generalize classical construction crossed products what call groupoid crossed products these coincide class strongly groupoid graded rings groupoid crossed products obtain generalization group graded situation groupoid graded bijection second cohomology group defined grading functor groupoid question picard groupoid collection equivalence classes rings strongly graded groupoid

Patrik Lundström  1

1 Department of Technology, Mathematics and Computer Science University West Gärdhemsvägen 4 Box 957 461 29, Trollhättan, Sweden 
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Patrik Lundström. Strongly groupoid graded rings and cohomology. Colloquium Mathematicum, Tome 106 (2006) no. 1, pp. 1-13. doi: 10.4064/cm106-1-1

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