Strong connections and the relative Chern-Galois character for corings

dc.creatorBöhm, Gabriella
dc.creatorBrzezinski, Tomasz
dc.date2005-03-22
dc.date2008-11-01
dc.date.accessioned2026-07-07T10:14:18Z
dc.date.available2026-07-07T10:14:18Z
dc.descriptionThe Chern-Galois theory is developed for corings or coalgebras over non-commutative rings. As the first step the notion of an entwined extension as an extension of algebras within a bijective entwining structure over a non-commutative ring is introduced. A strong connection for an entwined extension is defined and it is shown to be closely related to the Galois property and to the equivariant projectivity of the extension. A generalisation of the Doi theorem on total integrals in the framework of entwining structures over a non-commutative ring is obtained, and the bearing of strong connections on properties such as faithful flatness or relative injectivity is revealed. A family of morphisms between the K0-group of the category of finitely generated projective comodules of a coring and even relative cyclic homology groups of the base algebra of an entwined extension with a strong connection is constructed. This is termed a relative Chern-Galois character. Explicit examples include the computation of a Chern-Galois character of depth 2 Frobenius split (or separable) extensions over a separable algebra R. Finitely generated and projective modules are associated to an entwined extension with a strong connection, the explicit form of idempotents is derived, the corresponding (relative) Chern characters are computed, and their connection with the relative Chern-Galois character is explained.
dc.description34 pages, LaTeX. v3: Minor corrections in Examples 2.5 and 3.11
dc.identifierhttps://arxiv.org/abs/math/0503469
dc.identifierhttp://arxiv.org/abs/math/0503469
dc.identifierInt. Math. Res. Notices, 2005:42 (2005) 2579-2625
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172836
dc.subjectRings and Algebras
dc.subjectQuantum Algebra
dc.subject16W30
dc.titleStrong connections and the relative Chern-Galois character for corings
dc.typetext

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