Dlab's theorem and tilting modules for stratified algebras.

DOI10.1016/j.jalgebra.2006.08.041zbMath1127.16009OpenAlexW1999064940MaRDI QIDQ2456193

Anders Frisk

Publication date: 17 October 2007

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.08.041

zbMATH Keywords

tilting modulesfiltrationsquasi-hereditary algebrasfinitistic dimensioncostandard modulesstratified algebrasRingel duals

Mathematics Subject Classification ID

Representations of orders, lattices, algebras over commutative rings (16G30) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Representations of associative Artinian rings (16G10) Homological dimension in associative algebras (16E10)

Related Items (20)

Categorification of tensor powers of the vector representation of \(U_q(\mathfrak{gl}(1| 1))\) ⋮ KOSZUL DUALITY FOR STRATIFIED ALGEBRAS II. STANDARDLY STRATIFIED ALGEBRAS ⋮ Essential orders on stratified algebras with duality and \(\mathcal{S}\)-subcategories in \(\mathcal{O}\) ⋮ Standard stratifications of EI categories and Alperin's weight conjecture. ⋮ Ringel duality and Auslander-Dlab-Ringel algebras ⋮ Algebras stratified for all linear orders. ⋮ Strongly tilting truncated path algebras. ⋮ Semi-Infinite Highest Weight Categories ⋮ Projective-injective modules, Serre functors and symmetric algebras ⋮ Borelic pairs for stratified algebras ⋮ Cokernels of the Cartan matrix and stratifying systems ⋮ Some homological properties of category \(\mathcal{O}\). VI ⋮ Ringel duals of affine quasi-hereditary algebras ⋮ Categorification of (induced) cell modules and the rough structure of generalised Verma modules ⋮ Tilting modules, dominant dimensions and Brauer-Schur-Weyl duality ⋮ Parabolic category O for classical Lie superalgebras ⋮ Cohomological stratification of diagram algebras. ⋮ A diagram algebra for Soergel modules corresponding to smooth Schubert varieties ⋮ Extension Algebras of Standard Modules ⋮ A GENERALIZATION OF THE THEORY OF STANDARDLY STRATIFIED ALGEBRAS I: STANDARDLY STRATIFIED RINGOIDS

Cites Work

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• Stable equivalence for self-injective algebras and a generalization of tilting modules
• Quasi-hereditary algebras
• Reduction techniques for homological conjectures
• On a theorem of V. Dlab
• Applications of contravariantly finite subcategories
• Finitistic dimension of properly stratified algebras.
• Standardly stratified algebras and tilting
• The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences
• Standard stratifications of EI categories and Alperin's weight conjecture.
• MODULES OF FINITE PROJECTIVE DIMENSION FOR STANDARDLY STRATIFIED ALGEBRAS
• On the Relation Between Finitistic and Good Filtration Dimensions
• PROPERLY STRATIFIED ALGEBRAS AND TILTING
• TYPICAL BLOCKS OF THE CATEGORY $\mathcal{O}$ FOR THE QUEER LIE SUPERALGEBRA
• Finitistic dimension of standardly stratified algebras
• Properly stratified algebras
• Representation Theory of Artin Algebras II
• Stratifying endomorphism algebras

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