Stratifying Endomorphism Algebras.
Scott, Leonard.
Stratifying Endomorphism Algebras. - 1st ed. - 1 online resource (135 pages) - Memoirs of the American Mathematical Society ; v.124 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Introduction -- Chapter 1. Preliminaries -- 1.1. Endomorphism algebras -- 1.2. Duality -- 1.3. Idempotents and quotient categories -- 1.4. Filtrations and spectral sequences -- 1.5. Base change -- 1.6. On the modular representation theory of symmetric groups -- Chapter 2. Stratified algebras -- 2.1. Stratifications -- 2.2. Module-theoretic formulations -- 2.3. Stratified algebras and resolutions -- Chapter 3. Stratifying endomorphism algebras -- 3.1. Constructing stratified algebras -- 3.2. Filtrations and tilting modules -- 3.3. A converse result: stratified algebras as endomorphism algebras -- 3.4. Tilting modules and the Ringel dual of a highest weight category -- 3.5. Stratification and recollement -- 3.6. An abstract theory of twisted Young modules -- 3.7. An abstract theory of Specht module socles -- 3.8. Ext[sup(1)]-vanishing and abstract Specht/Weyl equivalences -- Chapter 4. Stratifications and orders in semisimple algebras -- 4.1. Integral endomorphism algebras -- 4.2. Z-stratified algebras -- 4.3. Integral stratification and recollement -- 4.4. An abstract theory of twisted integral Young modules -- 4.5. Integral theory and Specht module socles -- 4.6. Integral Ext[sup(1)]-vanishing and Specht/Weyl equivalences -- 4.7. Integral Ext[sup(1)]-vanishing and integral stratification -- Chapter 5. Examples -- 5.1. On the Dlab-Heath-Marko construction -- 5.2. Schur algebras -- 5.3. Singular categories -- 5.4. The category O -- Chapter 6. Some conjectures for finite Coxeter groups and further remarks -- 6.1. Example 1: finite groups-a stratification of length 2 -- 6.2. Example 2: the dihedral group of order 8 -- 6.3. A stratification conjecture -- 6.4. Stratifying systems -- a stronger conjecture -- References.
9781470401764
Linear algebraic groups.
Finite groups.
Representations of groups.
Electronic books.
QA179 -- .C556 1996eb
512/.55
Stratifying Endomorphism Algebras. - 1st ed. - 1 online resource (135 pages) - Memoirs of the American Mathematical Society ; v.124 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Introduction -- Chapter 1. Preliminaries -- 1.1. Endomorphism algebras -- 1.2. Duality -- 1.3. Idempotents and quotient categories -- 1.4. Filtrations and spectral sequences -- 1.5. Base change -- 1.6. On the modular representation theory of symmetric groups -- Chapter 2. Stratified algebras -- 2.1. Stratifications -- 2.2. Module-theoretic formulations -- 2.3. Stratified algebras and resolutions -- Chapter 3. Stratifying endomorphism algebras -- 3.1. Constructing stratified algebras -- 3.2. Filtrations and tilting modules -- 3.3. A converse result: stratified algebras as endomorphism algebras -- 3.4. Tilting modules and the Ringel dual of a highest weight category -- 3.5. Stratification and recollement -- 3.6. An abstract theory of twisted Young modules -- 3.7. An abstract theory of Specht module socles -- 3.8. Ext[sup(1)]-vanishing and abstract Specht/Weyl equivalences -- Chapter 4. Stratifications and orders in semisimple algebras -- 4.1. Integral endomorphism algebras -- 4.2. Z-stratified algebras -- 4.3. Integral stratification and recollement -- 4.4. An abstract theory of twisted integral Young modules -- 4.5. Integral theory and Specht module socles -- 4.6. Integral Ext[sup(1)]-vanishing and Specht/Weyl equivalences -- 4.7. Integral Ext[sup(1)]-vanishing and integral stratification -- Chapter 5. Examples -- 5.1. On the Dlab-Heath-Marko construction -- 5.2. Schur algebras -- 5.3. Singular categories -- 5.4. The category O -- Chapter 6. Some conjectures for finite Coxeter groups and further remarks -- 6.1. Example 1: finite groups-a stratification of length 2 -- 6.2. Example 2: the dihedral group of order 8 -- 6.3. A stratification conjecture -- 6.4. Stratifying systems -- a stronger conjecture -- References.
9781470401764
Linear algebraic groups.
Finite groups.
Representations of groups.
Electronic books.
QA179 -- .C556 1996eb
512/.55