Related papers: Recollement and Tilting Complexes
We investigate Tate cohomology of modules over a commutative noetherian ring with respect to semidualizing modules. We identify classes of modules admitting Tate resolutions and analyze the interaction between the corresponding relative and…
A Lefschetz module is a module over a graded algebra $A$ that satisfies analogues of Poincar\'{e} duality, the Hard Lefschetz property, and the Hodge--Riemann relations with respect to an open convex cone $\mathscr{K}$ in the degree one…
Let $\mathscr{C}$ be a $2$-Calabi-Yau triangulated category with two cluster tilting subcategories $\mathscr{T}$ and $\mathscr{U}$. Results by Demonet-Iyama-Jasso and J{\o}rgensen-Yakimov known as tropical duality says that the index with…
The separability tensor element of a separable extension of noncommutative rings is an idempotent when viewed in the correct endomorphism ring; so one speaks of a separability idempotent, as one usually does for separable algebras. It is…
We put cluster tilting in ageneral framework by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal one-orthogonal subcategory) carries an abelian structure. These abelian quotients turn out…
A key result in a 2004 paper by S. Arkhipov, R. Bezrukavnikov, and V. Ginzburg compares the bounded derived category of modules for the principal block of a Lusztig quantum enveloping algebra at anroot of unity with an explicit subcategory…
We shall show that the stable categories of graded Cohen-Macaulay modules over quotient singularities have tilting objects. In particular, these categories are triangle equivalent to derived categories of finite dimensional algebras. Our…
Many examples of nonpositively curved closed manifolds arise as blow-ups of projective hyperplane arrangements. If the hyperplane arrangement is associated to a finite reflection group W, and the blow-up locus is W-invariant, then the…
We study the problem of lifting and restricting TTF triples (equivalently, recollement data) for a certain wide type of triangulated categories. This, together with the parametrizations of TTF triples given in "Parametrizing recollement…
Let $A$ be a finite dimensional algebra over a field $k$ and $\textbf{P}$ be a 2-term silting complex in $K^{b}(\text{proj}A)$. In this paper, we investigate the representation dimension of $\text{End}_{D^{b}(A)} (\textbf{P})$ by using the…
This thesis establishes a generalised setting with which to unify the study of finite local complexity (FLC) patterns. The abstract notion of a "pattern" is introduced, which may be seen as an analogue of the space group of isometries…
We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number of (isoclasses of) these modules.
We show that the category of partial modules over a Hopf algebra $H$ is a biactegory (a bimodule category) over the category of global $H$-modules. The corresponding enrichment of partial modules over global modules is described, and the…
Let D be a triangulated category with a cluster tilting subcategory U. The quotient category D/U is abelian; suppose that it has finite global dimension. We show that projection from D to D/U sends cluster tilting subcategories of D to…
We introduce a generalization of tilting modules of finite projective dimension, projectively Wakamatsu tilting modules, which are self-orthogonal and Ext-progenerators in their Ext-perpendicular categories. Under a certain finiteness…
A commutative associative algebra $A$ over ${\mathbb C}$ with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for $A$ as a vertex algebra and the modules for $A$ as an…
We give a proof, based on the rigidity of tilting complexes, that the class of self-injective finite-dimensional algebras over an algebraically closed field is closed under derived equivalence.
We construct derived equivalences between group graded self-injective algebras, starting from equivalences between their 1-components, obtained via a construction of J. Rickard and S. Al-Nofayee.
Tilings of the plane resemble the simplicial and other complexes from algebraic topology, but have not been studied from this perspective. We construct finite categories corresponding to polygons with labeled directed edges, and introduce…
We construct quantization functors of quasi-Lie bialgebras. We establish a bijection between this set of quantization functors, modulo equivalence and twist equivalence, and the set of quantization functors of Lie bialgebras, modulo…