Strongly graded groupoids and strongly graded Steinberg algebras

JOURNAL OF ALGEBRA

卷:530

Article

Clark, Lisa Orloff¹  Hazrat, Roozbeh²  Rigby, Simon W.^3,4 

[1] Victoria Univ Wellington, Sch Math & Stat, Wellington, New Zealand

[2] Western Sydney Univ, Ctr Res Math, Penrith, NSW, Australia

[3] Univ Cape Town, Dept Math & Appl Math, Rondebosch, South Africa

[4] Univ Ghent, Dept Math Algebra & Geometry, Ghent, Belgium

关键词: Graded algebras;    Groupoids;    Steinberg algebras;    Leavitt path algebras;    Graded algebras;    Groupoids;    Steinberg algebras;    Leavitt path algebras;   

DOI  :  10.1016/j.jalgebra.2019.03.030

来源: Elsevier

【 摘 要 】

We study strongly graded groupoids, which are topological groupoids G equipped with a continuous, surjective functor kappa : G -> Gamma, to a discrete group Gamma, such that kappa(-1)(gamma)kappa(-1)(delta) = kappa(-1)(gamma delta), for all gamma, delta is an element of Gamma. We introduce the category of graded G-sheaves, and prove an analogue of Dade's Theorem: G is strongly graded if and only if every graded G-sheaf is induced by a G(epsilon)-sheaf. The Steinberg algebra of a graded ample groupoid is graded, and we prove that the algebra is strongly graded if and only if the groupoid is. Applying this result, we obtain a complete graphical characterisation of strongly graded Leavitt path and Kumjian-Pask algebras. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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