Exotic C*-algebras of geometric groups

2018/09/19 by Samei, Ebrahim, Wiersma, Matthew · 2 citations
#FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Operator Algebras (math.OA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1809.07007

Abstract

We consider a new class of potentially exotic group C*-algebras C^*_PFp^*(G) for a locally compact group G, and its connection with the class of potentially exotic group C*-algebras C^*_L^p(G) introduced by Brown and Guentner. Surprisingly, these two classes of C*-algebras are intimately related. By exploiting this connection, we show C^*_L^p(G)=C^*_PFp^*(G) for p∈ (2,∞), and the C*-algebras C^*_L^p(G) are pairwise distinct for p∈ (2,∞) when G belongs to a large class of nonamenable groups possessing the Haagerup property and either the rapid decay property or Kunze-Stein phenomenon by characterizing the positive definite functions that extend to positive linear functionals of C^*_L^p(G) and C^*_PFp^*(G). This greatly generalizes earlier results of Okayasu and the second author on the pairwise distinctness of C^*_L^p(G) for 20 (recall A_π⊆ B_π).

Cited by

• Rigidity of pseudofunction algebras of ample groupoids
• On the rate of exponential decay of coefficients on homogeneous spaces

Related

• On exotic group C*-algebras
• Exotic Crossed Products
• Exotic coactions
• Exotic \rm C^*-completions of étale groupoids
• Exotic group C*-algebras in noncommutative duality