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On Minimal Tilting Complexes in Highest Weight Categories
We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting...
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The Representation Theory of Brauer Categories I: Triangular Categories
This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of...
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Weight Modules
The theory of weight modules over reductive Lie algebras is a well-established branch of representation theory. For root-reductive Lie algebras, the...
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On Semisimplification of Tensor Categories
We develop the theory of semisimplifications of tensor categories defined by Barrett and Westbury. In particular, we compute the semisimplification...
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The Generalized Roof F(1, 2,n): Hodge Structures and Derived Categories
We consider generalized homogeneous roofs, i.e. quotients of simply connected, semisimple Lie groups by a parabolic subgroup, which admit two...
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NEW REALIZATIONS OF DEFORMED DOUBLE CURRENT ALGEBRAS AND DELIGNE CATEGORIES
In this paper, we propose an alternative construction of a certain class of Deformed Double Current Algebras. We construct them as spherical...
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M-traces in (Non-Unimodular) Pivotal Categories
We generalize the notion of a modified trace (or m-trace) to the setting of non-unimodular categories. M-traces are known to play an important role...
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New Constructions of Exceptional Simple Lie Superalgebras with Integer Cartan Matrix in Characteristics 3 and 5 via Tensor Categories
Using tensor categories, we present new constructions of several of the exceptional simple Lie superalgebras with integer Cartan matrix in...
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When the Schur functor induces a triangle-equivalence between Gorenstein defect categories
Let R be an Artin algebra and e be an idempotent of R . Assume that Tor
i eRe ( Re , G ) = 0 for any G ∈ Gproj eRe and i sufficiently large. Necessary... -
DERIVED CATEGORIES OF THE CAYLEY PLANE AND THE COADJOINT GRASSMANNIAN OF TYPE F
For the derived category of the Cayley plane, which is the cominuscule Grassmannian of Dynkin type E 6 , a full Lefschetz exceptional collection was...
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THE CATEGORY OF WEIGHT MODULES FOR SYMPLECTIC OSCILLATOR LIE ALGEBRAS
The rank n symplectic oscillator Lie algebra 𝔤 n is the semidirect product of the symplectic Lie algebra 𝔰𝔭 2 n and the Heisenberg algebra H n . In...
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External Vertices for Crystals of Affine Type A
We demonstrate that for a fixed dominant integral weight and fixed defect d , there are only a finite number of Morita equivalence classes of blocks...
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A Generalization of the Correspondences Between Quasi-Hereditary Algebras and Directed Bocses
Quasi-hereditary algebras were introduced by Cline, Parshall and Scott to study the highest weight categories in Lie theory. On the other hand,...