Inverse semigroup equivariant KK-theory and C^*-extensions

2015/08/12 by Bernhard Burgstaller, Burgstaller, Bernhard
Mathematics · #19K33 #19K35 #20M18 #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT #msc:19K33 #msc:19K35 #msc:20M18

paper · pdf · doi:10.48550/arxiv.1508.02998

arxiv created 2015/08/12 · arxiv updated 2015/08/13

Abstract

In this note we extend the classical result by G. G. Kasparov that the Kasparov groups KK₁(A,B) can be identified with the extension groups Ext(A,B) to the inverse semigroup equivariant setting. More precisely, we show that KK_G¹(A,B) ≅ Ext_G(A ⊗ \cal K_G,B ⊗ \cal K_G) for every countable, E-continuous inverse semigroup G. For locally compact second countable groups G this was proved by K. Thomsen, and technically this note presents an adaption of his proof.

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