Projective-injective modules, Serre functors and symmetric algebras

DOI10.1515/CRELLE.2008.020zbMath1235.16013arXivmath/0508119WikidataQ114053134 ScholiaQ114053134MaRDI QIDQ3524792

Volodymyr Mazorchuk, Catharina Stroppel

Publication date: 15 September 2008

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0508119

zbMATH Keywords

Schur algebrassemisimple Lie algebrasquasi-hereditary algebrascategory \(\mathcal O\)Serre functorsprojective-injective modulesdouble centraliser property

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Representations of associative Artinian rings (16G10)

Related Items (35)

Dualities and derived equivalences for category \(\mathcal{O}\) ⋮ Parabolic projective functors in type \(A\) ⋮ On functors associated to a simple root ⋮ Nazarov-Wenzl algebras, coideal subalgebras and categorified skew Howe duality ⋮ Ringel duality and Auslander-Dlab-Ringel algebras ⋮ Fayers’ conjecture and the socles of cyclotomic Weyl modules ⋮ Standard objects in 2-braid groups ⋮ Shuffling functors and spherical twists on \(D^{\mathrm{b}}(\mathcal{O}_0)\) ⋮ Some homological properties of category \(\mathcal{O}\). IV ⋮ Idempotent subquotients of symmetric quasi-hereditary algebras. ⋮ Equivariantization and Serre duality. I ⋮ The degenerate affine walled Brauer algebra ⋮ Simple transitive 2‐representations of Soergel bimodules for finite Coxeter types ⋮ Character \(D\)-modules via Drinfeld center of Harish-Chandra bimodules. ⋮ Serre functors for Lie algebras and superalgebras ⋮ Gale duality and Koszul duality ⋮ Hypertoric category \(\mathcal O\). ⋮ Symmetric functions, parabolic category \(\mathcal O\), and the Springer fiber. ⋮ Some homological properties of category \(\mathcal{O}\). VI ⋮ Ringel duals of affine quasi-hereditary algebras ⋮ Some homological properties of the category 𝒪, II ⋮ Knot invariants and higher representation theory ⋮ Categorification of (induced) cell modules and the rough structure of generalised Verma modules ⋮ Tilting modules, dominant dimensions and Brauer-Schur-Weyl duality ⋮ Categorification of a linear algebra identity and factorization of Serre functors ⋮ Generalized Serre duality ⋮ Categorification of tensor product representations of \(\mathfrak{sl}_k\) and category \(\mathcal{O}\) ⋮ On selfadjoint functors satisfying polynomial relations. ⋮ A categorification of integral Specht modules ⋮ A diagram algebra for Soergel modules corresponding to smooth Schubert varieties ⋮ Serre duality for Khovanov-Rozansky homology ⋮ Symmetric structure for the endomorphism algebra of projective-injective module in parabolic category ⋮ Centers of degenerate cyclotomic Hecke algebras and parabolic category 𝒪 ⋮ A categorification of the ribbon element in quantum \(sl(2)\) ⋮ Tilting modules for classical Lie superalgebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A decomposition theorem for certain self-dual modules in the category \(\mathcal O\)
• Notes on homological algebra and representations of Lie algebras
• Representations of Coxeter groups and Hecke algebras
• The Enright functor on the Bernstein-Gelfand-Gelfand category O
• Projective modules in the category \(\mathcal O\) for the Cherednik algebra.
• Category \({\mathcal O}\): gradings and translation functors.
• \(S\)-subcategories in \(O\)
• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism.
• Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors
• On Arkhipov's and Enright's functors.
• Applications of contravariantly finite subcategories
• A categorification of the Jones polynomial
• The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences
• On functors associated to a simple root
• Dlab's theorem and tilting modules for stratified algebras.
• Hecke algebras and characters of parabolic type of finite groups with (B, N)-pairs
• Noetherian hereditary abelian categories satisfying Serre duality
• Auslander-Reiten Triangles in Derived Categories of Finite-Dimensional Algebras
• Shuffled Verma Modules and Principal Series Modules over Complex Semisimple Lie Algebras
• Quasi-hereditary algebras which are dual extensions of algebras
• Finitistic dimension of standardly stratified algebras
• Quasi-Poisson Manifolds
• Translation and shuffling of projectively presentable modules and a categorification of a parabolic Hecke module
• Categories with projective functors
• Kategorie O , Perverse Garben Und Moduln Uber Den Koinvariantez Zur Weylgruppe
• Representation Theory of Artin Algebras I
• Category 𝒪: Quivers and endomorphism rings of projectives
• Twisting functors on 𝒪
• Koszul Duality Patterns in Representation Theory
• CROSSINGLESS MATCHINGS AND THE COHOMOLOGY OF (n, n) SPRINGER VARIETIES
• Kit algebras

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