Crossed products by twisted partial actions and graded algebras

Details Crossed products by twisted partial actions and graded algebras Crossed products by twisted partial actions and graded algebras

2008-06-24

arxiv.org/abs/0806.3898v1

J. Algebra, 320 (2008), 3278 - 3310

Mathematics

Rings and Algebras

38 pages, no figures

Scientific paper

For a twisted partial action \Theta of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A X_\Theta G is proved to be associative. Given a G-graded k-algebra B = \oplus_{g\in G}\B_g with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B_1 X_\Theta G for some twisted partial action of G on B_1. The equality B_g\B_{g^{-1}}B_g = \B_g for all g\in G is one of the ingredients of the criteria, and if it holds and, moreover, B has enough local units, then it is shown that B is stably isomorphic to a crossed product by a twisted partial action of G.

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