Flat connections and (co)modules

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dc.creatorBrzezinski, Tomasz
dc.date2006-08-07
dc.date2007-01-19
dc.date.accessioned2026-07-07T07:41:41Z
dc.date.available2026-07-07T07:41:41Z
dc.descriptionThe relationship between comodules of a coring and flat connections is reviewed. In particular we specialise to corings which are built on a tensor product of algebra and a coalgebra. Such corings are in one-to-one correspondence with entwining structures, and their comodules are entwined modules. These include Yetter-Drinfeld and anti-Yetter-Drinfeld modules and their generalisations, hence all the modules of interest to Hopf-cyclic cohomology. In this way the interpretation of the latter as modules with flat connections [A Kaygun and M Khalkhali, Hopf modules and noncommutative differential geometry, Lett. Math. Phys. 76 (2006), 77--91] is obtained as a corollary of a more general theory. We also introduce the notions of a connection in a comodule and of a bicomodule connection, and show how comodules with flat connections can be interpreted as modules of a C-ring. In this way all the above mentioned Hopf modules can be interpreted as comodules with flat connections.
dc.description18 pages, LaTeX; significantly expanded with two new sections on connections in (bi)comodules
dc.identifierhttps://arxiv.org/abs/math/0608170
dc.identifierhttp://arxiv.org/abs/math/0608170
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122205
dc.subjectQuantum Algebra
dc.subjectRings and Algebras
dc.subject16W30, 58B34
dc.titleFlat connections and (co)modules
dc.typetext

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