Strongly groupoid graded rings and cohomology

Patrik Lundström. "Strongly groupoid graded rings and cohomology." Colloquium Mathematicae 106.1 (2006): 1-13. <http://eudml.org/doc/284267>.

@article{PatrikLundström2006,
abstract = {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.},
author = {Patrik Lundström},
journal = {Colloquium Mathematicae},
keywords = {groupoid crossed products; strongly groupoid graded rings; invertible bimodules; Picard groupoids; cohomology groups; Morita contexts; bicategories},
language = {eng},
number = {1},
pages = {1-13},
title = {Strongly groupoid graded rings and cohomology},
url = {http://eudml.org/doc/284267},
volume = {106},
year = {2006},
}

TY - JOUR
AU - Patrik Lundström
TI - Strongly groupoid graded rings and cohomology
JO - Colloquium Mathematicae
PY - 2006
VL - 106
IS - 1
SP - 1
EP - 13
AB - 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.
LA - eng
KW - groupoid crossed products; strongly groupoid graded rings; invertible bimodules; Picard groupoids; cohomology groups; Morita contexts; bicategories
UR - http://eudml.org/doc/284267
ER -