Advanced search
1 file | 401.44 KB Add to list

Strongly graded groupoids and strongly graded Steinberg algebras

(2019) JOURNAL OF ALGEBRA. 530. p.34-68
Author
Organization
Abstract
We study strongly graded groupoids, which are topological groupoids G equipped with a continuous, surjective functor κ:G→Γ, to a discrete group Γ, such that κ−1(γ)κ−1(δ) = κ−1(γδ), for all γ, δ ∈ Γ. 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 Gε-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.
Keywords
Graded algebras, Groupoids, Steinberg algebras, Leavitt path algebras, C-ASTERISK-ALGEBRAS, LEAVITT PATH ALGEBRAS, KUMJIAN-PASK ALGEBRAS, INVERSE SEMIGROUP ALGEBRAS, MODULES, GRAPHS, RINGS

Downloads

  • 1711.04904.pdf
    • full text (Author's original)
    • |
    • open access
    • |
    • PDF
    • |
    • 401.44 KB

Citation

Please use this url to cite or link to this publication:

MLA
Clark, Lisa Orloff, et al. “Strongly Graded Groupoids and Strongly Graded Steinberg Algebras.” JOURNAL OF ALGEBRA, vol. 530, 2019, pp. 34–68.
APA
Clark, L. O., Hazrat, R., & Rigby, S. (2019). Strongly graded groupoids and strongly graded Steinberg algebras. JOURNAL OF ALGEBRA, 530, 34–68.
Chicago author-date
Clark, Lisa Orloff, Roozbeh Hazrat, and Simon Rigby. 2019. “Strongly Graded Groupoids and Strongly Graded Steinberg Algebras.” JOURNAL OF ALGEBRA 530: 34–68.
Chicago author-date (all authors)
Clark, Lisa Orloff, Roozbeh Hazrat, and Simon Rigby. 2019. “Strongly Graded Groupoids and Strongly Graded Steinberg Algebras.” JOURNAL OF ALGEBRA 530: 34–68.
Vancouver
1.
Clark LO, Hazrat R, Rigby S. Strongly graded groupoids and strongly graded Steinberg algebras. JOURNAL OF ALGEBRA. 2019;530:34–68.
IEEE
[1]
L. O. Clark, R. Hazrat, and S. Rigby, “Strongly graded groupoids and strongly graded Steinberg algebras,” JOURNAL OF ALGEBRA, vol. 530, pp. 34–68, 2019.
@article{8616807,
  abstract     = {We study strongly graded groupoids, which are topological groupoids G equipped with a continuous, surjective functor κ:G→Γ, to a discrete group Γ, such that κ−1(γ)κ−1(δ) = κ−1(γδ), for all γ, δ ∈ Γ. 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 Gε-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.},
  author       = {Clark, Lisa Orloff and Hazrat, Roozbeh and Rigby, Simon},
  issn         = {0021-8693},
  journal      = {JOURNAL OF ALGEBRA},
  keywords     = {Graded algebras,Groupoids,Steinberg algebras,Leavitt path algebras,C-ASTERISK-ALGEBRAS,LEAVITT PATH ALGEBRAS,KUMJIAN-PASK ALGEBRAS,INVERSE SEMIGROUP ALGEBRAS,MODULES,GRAPHS,RINGS},
  language     = {eng},
  pages        = {34--68},
  title        = {Strongly graded groupoids and strongly graded Steinberg algebras},
  url          = {http://dx.doi.org/10.1016/j.jalgebra.2019.03.030},
  volume       = {530},
  year         = {2019},
}

Altmetric
View in Altmetric
Web of Science
Times cited: