Category 𝒪: Quivers and endomorphism rings of projectives

DOI10.1090/S1088-4165-03-00152-3zbMath1050.17005OpenAlexW1674711990MaRDI QIDQ4826792

Catharina Stroppel

Publication date: 12 November 2004

Published in: Representation Theory of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1088-4165-03-00152-3

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Representations of quivers and partially ordered sets (16G20) Computational methods for problems pertaining to nonassociative rings and algebras (17-08)

Related Items (43)

Self Extensions of Simple Modules over Semisimple Lie Algebras ⋮ A Lie theoretic categorification of the coloured Jones polynomial ⋮ Dualities and derived equivalences for category \(\mathcal{O}\) ⋮ A structure theorem for Harish-Chandra bimodules via coinvariants and Golod rings ⋮ Parabolic projective functors in type \(A\) ⋮ Quivers with relations arising from Koszul algebras of \(\mathfrak g\)-invariants ⋮ On functors associated to a simple root ⋮ Categorified skew Howe duality and comparison of knot homologies ⋮ Perverse sheaves, Koszul IC-modules, and the quiver for the category \(\mathcal{O}\) ⋮ Tilting modules and cellular categories ⋮ Shuffling functors and spherical twists on \(D^{\mathrm{b}}(\mathcal{O}_0)\) ⋮ Some homological properties of category \(\mathcal{O}\). IV ⋮ The classification of blocks in BGG category \(\mathcal{O}\) ⋮ Tensor product algebras, Grassmannians and Khovanov homology ⋮ Highest weight categories arising from Khovanov's diagram algebra. IV: The general linear supergroup ⋮ Koszul duality and Soergel bimodules for dihedral groups ⋮ Categorifying fractional Euler characteristics, Jones-Wenzl projectors and \(3j\)-symbols ⋮ On category \(\mathcal O\) over triangular generalized Weyl algebras. ⋮ Projective-injective modules, Serre functors and symmetric algebras ⋮ Restriction to Levi subalgebras and generalization of the category \(\mathcal O\) ⋮ Quasi-hereditary algebras and generalized Koszul duality. ⋮ Gale duality and Koszul duality ⋮ BGG complexes in singular blocks of category \(\mathcal{O}\) ⋮ Symmetric functions, parabolic category \(\mathcal O\), and the Springer fiber. ⋮ Some homological properties of category \(\mathcal{O}\). VI ⋮ On representation-finite gendo-symmetric biserial algebras ⋮ 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 ⋮ Categorification of tensor product representations of \(\mathfrak{sl}_k\) and category \(\mathcal{O}\) ⋮ Parabolic category O for classical Lie superalgebras ⋮ Highest weight categories arising from Khovanov's diagram algebra. II: Koszulity ⋮ Localization algebras and deformations of Koszul algebras. ⋮ A diagram algebra for Soergel modules corresponding to smooth Schubert varieties ⋮ Symmetric structure for the endomorphism algebra of projective-injective module in parabolic category ⋮ A family of Koszul algebras arising from finite-dimensional representations of simple Lie algebras ⋮ Kostant Modules in Blocks of Category 𝒪_S ⋮ Some homological properties of category \(\mathcal{O}\). III ⋮ Algebraic properties of zigzag algebras ⋮ Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology ⋮ Quasi-hereditary algebras via generator-cogenerators of local self-injective algebras and transfer of Ringel duality. ⋮ Dimensions of irreducible modules over \(W\)-algebras and Goldie ranks

Cites Work

• Quasi-Frobenius rings and generalizations. QF-3 and QF-1 rings. Notes by Claus Michael Ringel
• Kazhdan-Lusztig conjecture and holonomic systems
• Representations of Coxeter groups and Hecke algebras
• Category of \(\mathfrak g\) modules
• The socle filtration of a Verma module
• The combinatorics of Harish-Chandra bimodules.
• Kategorie O , Perverse Garben Und Moduln Uber Den Koinvariantez Zur Weylgruppe
• Koszul Duality Patterns in Representation Theory
• Lie Group Representations on Polynomial Rings
• Double centralizer properties, dominant dimension, and tilting modules
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