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Ideals of Steinberg Algebras of Strongly Effective Groupoids, with Applications to Leavitt Path Algebras

Journal Article


Abstract


  • We consider the ideal structure of Steinberg algebras over a commutative ring with identity. We focus on Hausdorff groupoids that are strongly effective in the sense that their reductions to closed subspaces of their unit spaces are all effective. For such a groupoid, we completely describe the ideal lattice of the associated Steinberg algebra over any commutative ring with identity. Our results are new even for the special case of Leavitt path algebras; so we describe explicitly what they say in this context, and give two concrete examples.

UOW Authors


  •   Clark, Lisa Orloff (external author)
  •   Edie-Mitchell, Cain (external author)
  •   An Huef, Astrid (external author)
  •   Sims, Aidan

Publication Date


  • 2019

Citation


  • Clark, L., Edie-Mitchell, C., an Huef, A. & Sims, A. (2019). Ideals of Steinberg Algebras of Strongly Effective Groupoids, with Applications to Leavitt Path Algebras. Transactions Of The American Mathematical Society, 371 (8), 5461-5486.

Scopus Eid


  • 2-s2.0-85065108781

Number Of Pages


  • 25

Start Page


  • 5461

End Page


  • 5486

Volume


  • 371

Issue


  • 8

Place Of Publication


  • United States

Abstract


  • We consider the ideal structure of Steinberg algebras over a commutative ring with identity. We focus on Hausdorff groupoids that are strongly effective in the sense that their reductions to closed subspaces of their unit spaces are all effective. For such a groupoid, we completely describe the ideal lattice of the associated Steinberg algebra over any commutative ring with identity. Our results are new even for the special case of Leavitt path algebras; so we describe explicitly what they say in this context, and give two concrete examples.

UOW Authors


  •   Clark, Lisa Orloff (external author)
  •   Edie-Mitchell, Cain (external author)
  •   An Huef, Astrid (external author)
  •   Sims, Aidan

Publication Date


  • 2019

Citation


  • Clark, L., Edie-Mitchell, C., an Huef, A. & Sims, A. (2019). Ideals of Steinberg Algebras of Strongly Effective Groupoids, with Applications to Leavitt Path Algebras. Transactions Of The American Mathematical Society, 371 (8), 5461-5486.

Scopus Eid


  • 2-s2.0-85065108781

Number Of Pages


  • 25

Start Page


  • 5461

End Page


  • 5486

Volume


  • 371

Issue


  • 8

Place Of Publication


  • United States