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AN EXPLICIT FORMULA FOR A STRONG CONNECTION (2006)
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BibTeX
@MISC{Beggs06anexplicit,
author = {E. J. Beggs and Tomasz Brzezi Ński},
title = {AN EXPLICIT FORMULA FOR A STRONG CONNECTION},
year = {2006}
}
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Abstract
Abstract. An explicit formula for a strong connection form in a principal extension by a coseparable coalgebra is given. 1. In the studies of geometry of non-commutative principal bundles or coalgebra-Galois extensions (cf. [7]) an important role is played by the notion of a strong connection (for the universal differential structure) first introduced in the context of Hopf-Galois extensions in [10]. The existence of a strong connection guarantees that a bundle associated to a coalgebra-Galois extension is a (finitely generated and) projective module, hence it is (a module of sections on) a vector bundle in the sense of non-commutative geometry (cf. [9]). Furthermore, a strong connection form gives rise to a Chern-Galois character [6], a mapping from the Grothendieck group of isomorphism classes of finite dimensional corepresentations of the structure coalgebra to the cyclic homology of the base algebra (see [3] for the most general, relative formulation). The existence of a strong connection in a Hopf-Galois extension is assured by the classical Schneider Theorem I [15]. This states that a free coaction of a Hopf
Keyphrases
strong connection explicit formula hopf-galois extension coalgebra-galois extension strong connection form important role relative formulation structure coalgebra base algebra isomorphism class free coaction non-commutative geometry classical schneider theorem principal extension non-commutative principal bundle coseparable coalgebra finite dimensional corepresentations projective module chern-galois character universal differential structure grothendieck group vector bundle strong connection guarantee cyclic homology
