Twist deformations of module homomorphisms and connections

Schenkel, Alexander

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.

• Journal Article Type: Conference Paper
• 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