Starting from an arbitrary ring R we provide a systematic construction of ℤ/nℤ-graded rings A which are Frobenius extensions of R, and show that under mild assumptions, A is an Auslander-Gorenstein local ring if and only if so is R.
Let and be abelian categories with enough projective and injective objects, and a left exact additive functor. Then one has a comma category . It is shown that if is -exact, then is a (hereditary) cotorsion pair in and ) is a (hereditary) cotorsion pair in if and only if is a (hereditary) cotorsion pair in and and are closed under extensions. Furthermore, we characterize when special preenveloping classes in abelian categories and can induce special preenveloping classes...
We describe the structure of artin algebras for which all cycles of indecomposable modules are finite and almost all indecomposable modules have projective or injective dimension at most one.
We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain -algebras. We use well-developed homological techniques together with some niceties of the theory of locally convex spaces to generalize the results known in the case of Banach algebras and their inverse limits to wider classes of topological algebras. To this end we show that, for a continuous morphism ϕ: x → y of complexes of complete nuclear DF-spaces, the isomorphism of cohomology groups H...
We review recent progress in the study of cyclic cohomology of Hopf algebras, extended Hopf algebras, invariant cyclic homology, and Hopf-cyclic homology with coefficients, starting with the pioneering work of Connes-Moscovici.
In this article, we present two possible extensions of the classical theory of equivariant cohomology. The first, due to P. Baum, R. MacPherson and the author, is called the “delocalized theory". We attempt to present it in very concrete form for a circle action on a smooth manifold. The second is the cyclic homology of the crossed- product algebra of the algebra of smooth functions on a manifold, by the convolution algebra of smooth functions on a Lie group, when such Lie group act on the manifold....