Ideals of Steinberg algebras of strongly effective groupoids, with applications to Leavitt path algebras
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.
 Publication:

arXiv eprints
 Pub Date:
 January 2016
 arXiv:
 arXiv:1601.07238
 Bibcode:
 2016arXiv160107238O
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Operator Algebras;
 16S99 (Primary);
 16S10;
 22A22 (Secondary)