Six-Term Exact Sequences for Smooth Generalized Crossed Products

TL;DR

This paper introduces six-term exact sequences for smooth generalized crossed products, enabling computations of cyclic cohomology generators for quantum manifold subalgebras, using techniques from Pimsner algebras and Bott-periodicity.

Contribution

It establishes new six-term exact sequences for smooth generalized crossed products, extending tools for analyzing quantum and noncommutative geometries.

Findings

Derived six-term exact sequences for smooth generalized crossed products.

Applied sequences to compute cyclic cohomology generators of quantum Heisenberg manifolds.

Combined Pimsner algebra techniques with Bott-periodicity proofs.

Abstract

We define smooth generalized crossed products and prove six-term exact sequences of Pimsner-Voiculescu type. This sequence may, in particular, be applied to smooth subalgebras of the Quantum Heisenberg Manifolds in order to compute the generators of their cyclic cohomology. Our proof is based on a combination of arguments from the setting of (Cuntz-)Pimsner algebras and the Toeplitz proof of Bott-periodicity.