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Circle and Line Bundles Over Generalized Weyl Algebras
Tomasz Brzeziński,
Tomasz Brzezinski 
Algebras and Representation Theory, Volume: 19, Issue: 1, Pages: 57 - 69
Swansea University Author:
Tomasz Brzezinski
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DOI (Published version): 10.1007/s10468-015-9562-7
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...
| Published in: | Algebras and Representation Theory |
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| ISSN: | 1386-923X 1572-9079 |
| Published: |
2016
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| Online Access: |
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| 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. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
1 |
| Start Page: |
57 |
| End Page: |
69 |