Connections over twisted tensor products of algebras

Details Connections over twisted tensor products of algebras Connections over twisted tensor products of algebras

2006-10-31

arxiv.org/abs/math/0610978v2

International Mathematics Research Notices IMRN 2008 (7), Art. ID rnn005 (2008)

Mathematics

Quantum Algebra

19 pages, no figures. Minor style improvements and typos correction

Scientific paper

10.1093/imrn/rnn005

Motivated by some results in classical differential geometry, we give a constructive procedure for building up a connection over a (twisted) tensor product of two algebras, starting from connections defined on the factors. The curvature for the product connection is explicitly calculated, and shown to be independent of the choice of the twisting map and the module twisting map used to define the product connection. As a consequence, we obtain that a product of two flat connections is again a flat connection. We show that our constructions also behaves well with respect to bimodule structures, namely being the product of two bimodule connections again a bimodule connection. As an application of our theory, all the product connections on the quantum plane are computed.

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