Daniel Gonçalves

Leavitt Path Algebras as Partial Skew Group Rings

We realize Leavitt path algebras as partial skew group rings and give new proofs, based on partial skew group ring theory of the Cuntz–Krieger uniqueness theorem and simplicity criteria for Leavitt path algebras.

Simplicity of Partial Skew Group Rings of Abelian Groups

Let A be a ring with local units, E a set of local units for A, G an abelian group and α a partial action of G by ideals of A that contain local units and such that the partial skew group ring A ⋆α G is associative. We show that A ⋆α G is simple if and only if A is G-simple and the center of the corner eδ0(A ⋆α G)eδ0 is a field for all e ∈ E. We apply the result to characterize simplicity of partial skew group rings in two cases, namely for partial skew group rings arising from partial actions by clopen subsets of a compact set and partial actions on the set level. MSC2010: 16S35, 37B05Let

Partial crossed products as equivalence relation algebras

\A

Sliding block codes between shift spaces over infinite alphabets

be a ring with local units,

TWO-SIDED SHIFT SPACES OVER INFINITE ALPHABETS

\E

Free path groupoid grading on Leavitt path algebras

a set of local units for

Inverse semigroup shifts over countable alphabets

\A

Faithful Representations of Graph Algebras via Branching Systems

,

Bratteli–Vershik models for partial actions of ℤ

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On the representations of Leavitt path algebras

an abelian group and