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An Algebraic Analogue of Exel¿Pardo C ¿-Algebras

Journal Article


Abstract


  • We introduce an algebraic version of the Katsura C∗-algebra of a pair A,B of integer matrices and an algebraic version of the Exel–Pardo C∗-algebra of a self-similar action on a graph. We prove a Graded Uniqueness Theorem for such algebras and construct a homomorphism of the latter into a Steinberg algebra that, under mild conditions, is an isomorphism. Working with Steinberg algebras over non-Hausdorff groupoids we prove that in the unital case, our algebraic version of Katsura C∗-algebras are all isomorphic to Steinberg algebras.

Publication Date


  • 2021

Citation


  • Hazrat, R., Pask, D., Sierakowski, A., & Sims, A. (2021). An Algebraic Analogue of Exel¿Pardo C ¿-Algebras. Algebras and Representation Theory, 24(4), 877-909. doi:10.1007/s10468-020-09973-x

Scopus Eid


  • 2-s2.0-85087072424

Web Of Science Accession Number


Start Page


  • 877

End Page


  • 909

Volume


  • 24

Issue


  • 4

Abstract


  • We introduce an algebraic version of the Katsura C∗-algebra of a pair A,B of integer matrices and an algebraic version of the Exel–Pardo C∗-algebra of a self-similar action on a graph. We prove a Graded Uniqueness Theorem for such algebras and construct a homomorphism of the latter into a Steinberg algebra that, under mild conditions, is an isomorphism. Working with Steinberg algebras over non-Hausdorff groupoids we prove that in the unital case, our algebraic version of Katsura C∗-algebras are all isomorphic to Steinberg algebras.

Publication Date


  • 2021

Citation


  • Hazrat, R., Pask, D., Sierakowski, A., & Sims, A. (2021). An Algebraic Analogue of Exel¿Pardo C ¿-Algebras. Algebras and Representation Theory, 24(4), 877-909. doi:10.1007/s10468-020-09973-x

Scopus Eid


  • 2-s2.0-85087072424

Web Of Science Accession Number


Start Page


  • 877

End Page


  • 909

Volume


  • 24

Issue


  • 4