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Circle and Line Bundles Over Generalized Weyl Algebras / Tomasz BrzeziƄski; Tomasz Brzezinski

Algebras and Representation Theory, Volume: 19, Issue: 1, Pages: 57 - 69

Swansea University Author: Tomasz, Brzezinski

Abstract

Strongly Z-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras B(p;q,0) (over a ring of polynomials in one variable) are constructed. The Chern-Connes pairing between the cyclic cohomology of B(p;q,0) and the isomo...

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Published in: Algebras and Representation Theory
ISSN: 1386-923X 1572-9079
Published: 2016
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa22634
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Abstract: Strongly Z-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras B(p;q,0) (over a ring of polynomials in one variable) are constructed. The Chern-Connes pairing between the cyclic cohomology of B(p;q,0) and the isomorphism classes of sections of associated line bundles over B(p;q,0) is computed, thus demonstrating that these bundles, which are labelled by integers, are non-trivial and mutually non- isomorphic. The constructed strongly Z-graded algebras are shown to have Hochschild cohomology reminiscent of that of Calabi-Yau algebras. The paper is supplemented by an observation that a grading by an Abelian group in the middle of a short exact sequence is strong if and only if the induced gradings by the outer groups in the sequence are strong.
College: College of Science
Issue: 1
Start Page: 57
End Page: 69