Crossed products by twisted partial actions and graded algebras

By Mikhailo Dokuchaev, R. Exel, J. Simón. 2008

67 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3a87601a38b8f68707bf060dd661b9f714abdd98

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Recent developments around partial actions (2018, methodology): “ the unit ﬁber algebra is stable), is a C∗-crossed product of the unit ﬁber algebra by a continuous partial action of the base group [149]. The algebraic version of the latter fact was established in [121]. This algebraic concept was applied to Hecke algebras in [153], where, among other results, it”
Partial Dynamical Systems, Fell Bundles and Applications (2015, background): “[47], [100], [34], [11], [35], [85], [36], [21], [22] and [37].”