相关论文: Homological algebra in bivariant K-theory and othe…
In this paper, we consider compatible Hom-associative algebras as a twisted version of compatible associative algebras. Compatible Hom-associative algebras are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie…
Let l be a commutative ring with unit. Garkusha constructed a functor from the category of l-algebras into a triangulated category D, that is a universal excisive and homotopy invariant homology theory. Later on, he provided different…
This note proposes a new method to complete a triangulated category, which is based on the notion of a Cauchy sequence. We apply this to categories of perfect complexes. It is shown that the bounded derived category of finitely presented…
We give criteria for subcategories of a compactly generated algebraic triangulated category to be precovering or preenveloping. These criteria are formulated in terms of closure conditions involving products, coproducts, directed homotopy…
We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…
We provide a foundation for working with homological and homotopical methods in categorical algebra. This involves two mutually complementary components, namely (a) the strategic selection of suitable axiomatic frameworks, some well known…
By counting with triangles and the octohedral axiom, we find a direct way to prove the formula of To\"en in \cite{Toen2005} for a triangulated category with (left) homological-finite condition.
We compute the group homology, the topological K-theory of the reduced C^*-algebra, the algebraic K-theory and the algebraic L-theory of the group ring of the semi-direct product of the three-dimensional discrete Heisenberg group by Z/4.…
In this article, a new construction of derived equivalences is given. It relates different endomorphism rings and more generally cohomological endomorphism rings - including higher extensions - of objects in triangulated categories. These…
The category of rational G-equivariant cohomology theories for a compact Lie group $G$ is the homotopy category of rational G-spectra and therefore tensor-triangulated. We show that its Balmer spectrum is the set of conjugacy classes of…
For every regular cardinal $\alpha$, we construct a cofibrantly generated Quillen model structure on a category whose objects are essentially DG categories which are stable under suspensions, cosuspensions, cones and $\alpha$-small sums.…
The equivariant coarse index is well-understood and widely used for actions by discrete groups. We extend the definition of this index to general locally compact groups. We use a suitable notion of admissible modules over $C^*$-algebras of…
We formulate a version of Baum-Connes' conjecture for a discrete quantum group, building on our earlier work (\cite{GK}). Given such a quantum group $\cla$, we construct a directed family $\{\cle_F \}$ of $C^*$-algebras ($F$ varying over…
Extriangulated categories axiomatize extension-closed subcategories of triangulated categories. We show that the homotopy category of an exact quasi-category can be equipped with a natural extriangulated structure.
We introduce the notion of homological systems $\Theta$ for triangulated categories. Homological systems generalize, on one hand, the notion of stratifying systems in module categories, and on the other hand, the notion of exceptional…
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
We extend results of Br\"ustle-Yang on ideal quotients of 2-term subcategories of perfect derived categories of non-positive dg algebras to a relative setting. We find a new interpretation of such quotients: they appear as prototypical…
Replaces Previous version. Includes comments on poincare duality for twisted equivariant in the context of proper and discrete actions and the Baum-Connes Conjecture. We use a spectral sequence proposed by C. Dwyer and previous work by…
We construct a surjective homomorphism from Somekawa's K-group associated to a finite collection of semi-abelian varieties over a perfect field to a corresponding Hom group in Voevodsky's triangulated category of effective motivic…
We define and study an analogue of the Baum-Connes assembly map for complex semisimple quantum groups, that is, Drinfeld doubles of $ q $-deformations of compact semisimple Lie groups. Our starting point is the deformation picture of the…