منابع مشابه
Hom-bialgebras and Comodule Algebras
We construct a Hom-bialgebra M(2) representing the functor of 2 × 2-matrices on Hom-associative algebras. We also construct a Hom-algebra analogue of the affine plane and show that it is a comodule Hom-algebra over M(2) in a suitable sense.
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Principal comodule algebras can be thought of as objects representing principal bundles in non-commutative geometry. A crucial component of a principal comodule algebra is a strong connection map. For some applications it suffices to prove that such a map exists, but for others, such as computing the associated bundle projectors or Chern–Galois characters, an explicit formula for a strong conne...
متن کاملProjectivity and freeness over comodule algebras
Let H be a Hopf algebra and A an H-simple right H-comodule algebra. It is shown that under certain hypotheses every (H,A)-Hopf module is either projective or free as an A-module and A is either a quasi-Frobenius or a semisimple ring. As an application it is proved that every weakly finite (in particular, every finite dimensional) Hopf algebra is free both as a left and a right module over its f...
متن کاملSkew group algebras of piecewise hereditary algebras are piecewise hereditary
The aim of this paper is twofold. First, we show that the main results of HappelRickard-Schofield (1988) and Happel-Reiten-Smalø (1996) on piecewise hereditary algebras are coherent with the notion of group action on an algebra. Then, we take advantage of this compatibility and show that if G is a finite group acting on a piecewise hereditary algebra A over an algebraically closed field whose c...
متن کاملCyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras
In this paper we construct a cylindrical module A♮H for an Hcomodule algebra A, where the antipode of the Hopf algebra H is bijective. We show that the cyclic module associated to the diagonal of A♮H is isomorphic with the cyclic module of the crossed product algebra A ⋊H. This enables us to derive a spectral sequence for the cyclic homology of the crossed product algebra. We also construct a c...
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ژورنال
عنوان ژورنال: Journal of Noncommutative Geometry
سال: 2011
ISSN: 1661-6952
DOI: 10.4171/jncg/88