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Erratum to: Groupoid algebras as cuntz-pimsner algebras (Mathematica Scandinavica (2018) 120: 1 (115¿123) DOI: 10.7146/math.scand.a-25507)

Journal Article


Abstract


  • In the published version [1], Lemma 9 (2) and (3) say(2) ker(φ) ⊥ = C * r (G0) ∩ C0({g ∈ G0 : s(g) ∈ r(G1)}) = span{fg * : f, g ∈ Cc(G1)}; (3) φX(G)(a) ∈ K (X(G)) for all a ∈ C * r (G), and the Katsura ideal JX(G) is JX(G) = span{fg * : f, g ∈ Cc(G1)}. These statements are incorrect and should be replaced with (2) ker(φ) ⊥ = C * r (G0) ∩ C0({g ∈ G0 : s(g) ∈ r(G1)}), and span{fg * : f, g ∈ Cc(G1)} ⊆ ker(φ) ⊥ with equality if r(G1) is closed; (3) the Katsura ideal JX(G) is JX(G) = span{fg * : f, g ∈ Cc(G1)}. This entails modifications to the proofs of these statements as well. For details we refer the reader to Lemma 9 and Remark 10 of the updated arXiv version https://arxiv.org/abs/1402.7126v2. We thank James Fletcher for bringing the error to our attention.

Publication Date


  • 2018

Citation


  • Rennie, A., Robertson, D., & Sims, A. (2018). Erratum to: Groupoid algebras as cuntz-pimsner algebras (Mathematica Scandinavica (2018) 120: 1 (115¿123) DOI: 10.7146/math.scand.a-25507). Mathematica Scandinavica, 123(1), 160. doi:10.7146/math.scand.a-105830

Scopus Eid


  • 2-s2.0-85051081155

Web Of Science Accession Number


Start Page


  • 160

Volume


  • 123

Issue


  • 1

Abstract


  • In the published version [1], Lemma 9 (2) and (3) say(2) ker(φ) ⊥ = C * r (G0) ∩ C0({g ∈ G0 : s(g) ∈ r(G1)}) = span{fg * : f, g ∈ Cc(G1)}; (3) φX(G)(a) ∈ K (X(G)) for all a ∈ C * r (G), and the Katsura ideal JX(G) is JX(G) = span{fg * : f, g ∈ Cc(G1)}. These statements are incorrect and should be replaced with (2) ker(φ) ⊥ = C * r (G0) ∩ C0({g ∈ G0 : s(g) ∈ r(G1)}), and span{fg * : f, g ∈ Cc(G1)} ⊆ ker(φ) ⊥ with equality if r(G1) is closed; (3) the Katsura ideal JX(G) is JX(G) = span{fg * : f, g ∈ Cc(G1)}. This entails modifications to the proofs of these statements as well. For details we refer the reader to Lemma 9 and Remark 10 of the updated arXiv version https://arxiv.org/abs/1402.7126v2. We thank James Fletcher for bringing the error to our attention.

Publication Date


  • 2018

Citation


  • Rennie, A., Robertson, D., & Sims, A. (2018). Erratum to: Groupoid algebras as cuntz-pimsner algebras (Mathematica Scandinavica (2018) 120: 1 (115¿123) DOI: 10.7146/math.scand.a-25507). Mathematica Scandinavica, 123(1), 160. doi:10.7146/math.scand.a-105830

Scopus Eid


  • 2-s2.0-85051081155

Web Of Science Accession Number


Start Page


  • 160

Volume


  • 123

Issue


  • 1