Crossed products by twisted partial actions and graded algebras

作者：M. Dokuchaev, R. Exel, J. Simón · 年份：2008 · DOI：10.1016/J.JALGEBRA.2008.06.023 · 被引用次数：67 · 研究领域：Mathematics

Abstract For a twisted partial action Θ of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A ⋊ Θ G is proved to be associative. Given a G-graded k-algebra B = ⊕ g ∈ 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 ⋊ Θ G for some twisted partial action of G on B 1 . The equality B g B g −1 B g = B g ( ∀ g ∈ 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.