ALEXANDER SCHENKEL ALEXANDER.SCHENKEL@NOTTINGHAM.AC.UK
Associate Professor
Twist deformations of module homomorphisms and connections
Schenkel, Alexander
Authors
Abstract
Let H be a Hopf algebra, A a left H-module algebra and V a left H-module A-bimodule. We study the behavior of the right A-linear endomorphisms of V under twist deformation. We in particular construct a bijective quantization map to the right A_\star-linear endomorphisms of V_\star, with A_\star,V_\star denoting the usual twist deformations of A,V. The quantization map is extended to right A-linear homomorphisms between left H-module A-bimodules and to right connections on V. We then investigate the tensor product of linear maps between left H-modules. Given a quasitriangular Hopf algebra we can define an H-covariant tensor product of linear maps, which restricts for left H-module A-bimodules to a well-defined tensor product of right A-linear homomorphisms on tensor product modules over A. This also requires a quasi-commutativity condition on the algebra and bimodules. Using this tensor product we can construct a new lifting prescription of connections to tensor product modules, generalizing the usual prescription to also include nonequivariant connections.
Citation
Schenkel, A. (2012). Twist deformations of module homomorphisms and connections. Proceedings of Science, 155, Article PoS(CORFU2011)056. https://doi.org/10.22323/1.155.0056
Presentation Conference Type | Conference Paper (published) |
---|---|
Conference Name | Corfu Summer Institute 2011 |
Acceptance Date | Aug 2, 2012 |
Online Publication Date | Aug 14, 2012 |
Publication Date | Aug 14, 2012 |
Deposit Date | Sep 11, 2019 |
Publicly Available Date | Nov 4, 2019 |
Publisher | Sissa Medialab |
Peer Reviewed | Peer Reviewed |
Volume | 155 |
Article Number | PoS(CORFU2011)056 |
DOI | https://doi.org/10.22323/1.155.0056 |
Keywords | Quantum Algebra; High Energy Physics - Theory; Mathematical Physics |
Public URL | https://nottingham-repository.worktribe.com/output/2460576 |
Publisher URL | https://pos.sissa.it/155/056 |
Contract Date | Nov 4, 2019 |
Files
CORFU2011_056
(274 Kb)
PDF
Publisher Licence URL
https://creativecommons.org/licenses/by-sa/3.0/
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