The cycline subalgebra of a Kumjian-Pask algebra

Clark, Lisa Orloff; Canto, Cristóbal Gil; Nasr-Isfahani, Alireza

doi:10.1090/proc/13439

Cited by 5 publications

(1 citation statement)

References 16 publications

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“…Our uniqueness theorem says that a Steinberg algebra homomorphism is injective if and only if it is injective on the interior of the isotropy group bundle. This generalises theorems [18,Theorem 5.2] and [11,Theorem 5.4] for Leavitt path algebras and Kumjian-Pask algebras respectively.…”

Section: Introductionsupporting

confidence: 70%

A generalized uniqueness theorem and the graded ideal structure of Steinberg algebras

2017

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Given an ample, Hausdorff groupoid {\mathcal{G}}, and a unital commutative ring R, we consider the Steinberg algebra {A_{R}(\mathcal{G})}. First we prove a uniqueness theorem for this algebra and then, when {\mathcal{G}} is graded by a cocycle, we study graded ideals in {A_{R}(\mathcal{G})}. Applications are given for two classes of ample groupoids, namely those coming from actions of groups on graphs, and also to groupoids defined in terms of Boolean dynamical systems.

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Section: Introductionsupporting

confidence: 70%

A generalized uniqueness theorem and the graded ideal structure of Steinberg algebras

2017

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Representing k-graphs as Matrix Algebras

Rosjanuardi

2018

J. Phys.: Conf. Ser.

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Abstract. For any commutative unital ring R and finitely aligned k-graph Λ with |Λ| < ∞ without cycles, we can realise Kumjian-Pask algebra ‫ܲܭ‬ ோ (Λ) as a direct sum of of matrix algebra over some vertices v with properties ‫}ݒ{‬ = ‫ݒ‬Λ , i.e: ⊕ ௩Λୀ{௩} ‫ܯ‬ |Λ௩| (ܴ) . When there is only a single vertex ‫ݒ‬ ∈ Λ such that ‫}ݒ{‬ = ‫ݒ‬Λ, we can realise the Kumjian-Pask algebra as the matrix algebra ‫ܯ‬ |Λ௩| (ܴ). Hence the matrix algebra ‫ܯ‬ |௩Λ| (ܴ) can be regarded as a representation of the k-graph Λ. In this talk we will figure out the relation between finitely aligned k-graph and matrix algebra.

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A note on the centralizer of a subalgebra of the Steinberg algebra

Hazrat

2021

St. Petersburg Math. J.

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For an ample Hausdorff groupoid G \mathcal {G} , and the Steinberg algebra A R ( G ) A_R(\mathcal {G}) with coefficients in the commutative ring R R with unit, the centralizer is described for the subalgebra A R ( U ) A_R(U) with U U an open closed invariant subset of the unit space of G \mathcal {G} . In particular, it is shown that the algebra of the interior of the isotropy is indeed the centralizer of the diagonal subalgebra of the Steinberg algebra. This will unify several results in the literature, and the corresponding results for Leavitt path algebras follow.

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The cycline subalgebra of a Kumjian-Pask algebra

Cited by 5 publications

References 16 publications

A generalized uniqueness theorem and the graded ideal structure of Steinberg algebras

A generalized uniqueness theorem and the graded ideal structure of Steinberg algebras

Representing k-graphs as Matrix Algebras

A note on the centralizer of a subalgebra of the Steinberg algebra

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