Cyclic homology and equivariant homology.
Cyclic homology and equivariant theories
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....
Cyclic homology and the Lie algebra homology of matrices.
Cyclic homology of group rings
Cyclic homology of groups and the Bass conjecture.
D (...)+ and the Arting cokernel.
Decomposition of the Grothendieck group of stable categories of finite groups.
Decompositions of the category of noncommutative sets and Hochschild and cyclic homology
In this note we show that the main results of the paper [PR] can be obtained as consequences of more general results concerning categories whose morphisms can be uniquely presented as compositions of morphisms of their two subcategories with the same objects. First we will prove these general results and then we will apply it to the case of finite noncommutative sets.
Deformation theory via deviations
Deformations of bimodule problems
We prove that deformations of tame Krull-Schmidt bimodule problems with trivial differential are again tame. Here we understand deformations via the structure constants of the projective realizations which may be considered as elements of a suitable variety. We also present some applications to the representation theory of vector space categories which are a special case of the above bimodule problems.
Derivations, semidirect products and reduced cyclic cohomology.
Derived dimension via -tilting theory
Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support -tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given -tilting module.
Derived equivalence classification of weakly symmetric algebras of domestic type
We complete the derived equivalence classification of all weakly symmetric algebras of domestic type over an algebraically closed field, by solving the problem of distinguishing standard and nonstandard algebras up to stable equivalence, and hence derived equivalence. As a consequence, a complete stable equivalence classification of weakly symmetric algebras of domestic type is obtained.
Derived equivalences between generalized matrix algebras
We construct derived equivalences between generalized matrix algebras. We record several corollaries. In particular, we show that the -replicated algebras of two derived equivalent, finite-dimensional algebras are also derived equivalent.
Diagonal reductions of matrices over exchange ideals
In this paper, we introduce related comparability for exchange ideals. Let be an exchange ideal of a ring . If satisfies related comparability, then for any regular matrix , there exist left invertible and right invertible such that for idempotents .
Die Struktur von projektiven Moduln.
Die Zentren hereditärer Ringe.
Différentielles non commutatives et théorie de Galois différentielle ou aux différences
Dimension homologique de modules simples
Dimension injective des produits croisés.