Pimsner algebras and Gysin sequences from principal circle actions

Abstract

A self Morita equivalence over an algebra B, given by a B-bimodule E, is thought of as a line bundle over B. The corresponding Pimsner algebra O_E is then the total space algebra of a noncommutative principal circle bundle over B. A natural Gysin-like sequence relates the KK-theories of O_E and of B. Interesting examples come from O_E a quantum lens space over B a quantum weighted projective line (with arbitrary weights). The KK-theory of these spaces is explicitly computed and natural generators are exhibited.

29 pages. v2: Scientific content unchanged. Exposition improved. Added references. To appear in the JNcG

References in corpus (1)

• Spectral Triples and Generalized Crossed Products

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