Morita equivalence of two ℓ^p Roe-type algebras

2023/06/26 by Yeong Chyuan Chung, Chung, Yeong Chyuan
Mathematics · #46L80 #47L10 (Primary) #51F30 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2306.14721

openalex publication_date 2023/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a metric space with bounded geometry, one may associate with it the ℓ^p uniform Roe algebra and the ℓ^p uniform algebra, both containing information about the large scale geometry of the metric space. We show that these two Banach algebras are Morita equivalent in the sense of Lafforgue for 1≤ p<∞. As a consequence, these two Banach algebras have the same K-theory. We then define an ℓ^p uniform coarse assembly map taking values in the K-theory of the ℓ^p uniform Roe algebra and show that it is not always surjective.

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