Related papers: Based quasi-hereditary algebras
We define and study new classes of quasi-hereditary and cellular algebras which generalize Turner's double algebras. Turner's algebras provide a local description of blocks of symmetric groups up to derived equivalence. Our general…
We prove that cellular Noetherian algebras with finite global dimension are split quasi-hereditary over a regular commutative Noetherian ring with finite Krull dimension and their quasi-hereditary structure is unique, up to equivalence. In…
We obtain a presentation by generators and relations for generalized Schur algebras and their quantizations. This extends earlier results obtained in the type A case. The presentation is compatible with Lusztig's modified form of a…
Given an algebra and a finite group acting on it via automorphisms, a natural object of study is the associated skew group algebra. In this article, we study the relationship between quasi-hereditary structures on the original algebra and…
Dlab and Ringel showed that algebras being quasi-hereditary in all orders for indices of primitive idempotents becomes hereditary. So, we are interested in for which orders a given quasi-hereditary algebra is again quasi-hereditary. As a…
Not every quasihereditary algebra $(A,\Phi,\unlhd)$ has an exact Borel subalgebra. A theorem by Koenig, K\"ulshammer and Ovsienko asserts that there always exists a quasihereditary algebra Morita equivalent to $A$ that has a regular exact…
Let $A$ be a finite dimensional algebra over an algebraically closed field $\mathbf{k}$. If $A$ is quasi-hereditary and the projective dimensions of all standard modules are at most one, then $A$ is called left strongly quasi-hereditary. In…
Quasi-hereditary algebras were introduced by Cline, Parshall and Scott to describe the highest weight categories of representations of semisimple Lie algebras and algebraic groups by the module categories of finite-dimensional algebras.…
We propose an extension of the theory of parity sheaves, which allows for non-locally constant sheaves along strata. Our definition is tailored for proving the existence of (proper, quasihereditary, etc) stratifications of…
We introduce the notion of a cellular system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for an algebra to be quasi-hereditary is the existence of a full divisible cellular…
A cell algebra structure is found for a family of generalized Schur algebras previously studied by the author. This cell algebra structure is then used to construct the irreducible representations of these algebras and to determine when the…
The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolving subcategory containing all standard modules over split…
A quasi-hereditary algebra is an Artin algebra together with a partial order on its set of isomorphism classes of simple modules which satisfies certain conditions. In this article we investigate all the possible choices that yield to…
A quasi-hereditary algebra is an algebra equipped with a certain partial order $\unlhd$ on its simple modules. Such a partial order -- called a quasi-hereditary structure -- gives rise to a characteristic tilting module $T_{\unlhd}$ by a…
Dlab and Ringel showed that algebras being quasi-hereditary in all total orders for indices of primitive idempotents becomes hereditary. So, we are interested in for which orders a given quasi-hereditary algebra is again quasi-hereditary.…
Establishing whether an algebra is quasi-hereditary or not is, in general, a difficult problem. In this paper we introduce a sufficient criterion to determine whether a general finite dimensional algebra is quasi-hereditary by showing that…
Highest weight categories arising in Lie theory are known to be associated with finite dimensional quasi-hereditary algebras such as Schur algebras or blocks of category $\mathcal O$. An analogue of the PBW theorem will be shown to hold for…
A category is called {\em split} if for every morphism $s\colon X\to Y$ there exists a morphism $t\colon Y\to X$ such that $s\circ t\circ s = s$. Let $C$ be a finite split category, let $k$ be a field of characteristic 0 and let $\alpha$ be…
Motivated by the structure of the algebras associated to the blocks of the BGG-category O we define a subclass of quasi-hereditary algebras called 1-quasi-hereditary. Many properties of these algebras only depend on the defining partial…
We compute the Hochschild cohomology of any block of $q$-Schur algebras. We focus the even part of this Hochschild cohomology ring. To compute the Hochschild cohomology of $q$-Schur algebras, we prove the following two results: first, we…