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On the relation between the product of KK-groups and the KK-group of the product
Abstract
We observe that the canonical map KK(A, ∏n ∈ ℕ Bn) → ∏n ∈ ℕ KK(A,Bn) is an isomorphism of abelian groups whenever A enjoys the Universal Coefficient Theorem and Bn are unital, simple and purely infinite C*-algebras. This clarifies an aspect of previous work of Dadarlat--Eilers and Tikuisis--White--Winter.
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BibTeX
@misc{martinez2026relation,
title = {{On the relation between the product of KK-groups and the KK-group of the product}},
author = {Diego Martínez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.20181},
eprint = {2606.20181},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.20181},
}
RIS
TY - UNPB
TI - On the relation between the product of KK-groups and the KK-group of the product
AU - Diego Martínez
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2606.20181
UR - https://arxiv.org/abs/2606.20181
AB - We observe that the canonical map KK(A, ∏_n ∈ ℕ B_n) → ∏_n ∈ ℕ KK(A,B_n) is an isomorphism of abelian groups whenever A enjoys the Universal Coefficient Theorem and B_n are unital, simple and purely infinite C*-algebras. This clarifies an aspect of previous work of Dadarlat--Eilers and Tikuisis--White--Winter.
ER -