Document Zbl 0888.16006 - zbMATH Open
Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.
Fields
| any | anywhere |
| an | internal document identifier |
| au | author, editor |
| ai | internal author identifier |
| ti | title |
| la | language |
| so | source |
| ab | review, abstract |
| py | publication year |
| rv | reviewer |
| cc | MSC code |
| ut | uncontrolled term |
| dt | document type (j: journal article; b: book; a: book article) |
Operators
| a & b | logic and |
| a | b | logic or |
| !ab | logic not |
| abc* | right wildcard |
| "ab c" | phrase |
| (ab c) | parentheses |
See also our General Help.
Stratifying endomorphism algebras. (English) Zbl 0888.16006
From the abstract: Suppose that \(R\) is a finite dimensional algebra and \(T\) is a right \(R\)-module. Let \(A=\text{End}_R(T)\) be the endomorphism algebra of \(T\). This paper presents a systematic study of the relationships between the representation theories of \(R\) and \(A\), especially those involving actual or potential quasi-hereditary structures on the latter algebra. Our original motivation comes from the theory of Schur algebras, work of Soergel on the Bernstein-Gelfand-Gelfand category \(\mathcal O\), and recent results of Dlab-Heath-Marko realizing certain endomorphism algebras as quasi-hereditary algebras.
Besides synthesizing common features of all these examples, we go beyond them in a number of new directions. Some examples involve new results in theory of tilting modules, an abstract “Specht/Weyl module” correspondence, a new theory of stratified algebras, and a deformation theory based on the study of orders in semisimple algebras. Our approach reconceptualizes most of the modular representation theory of symmetric groups involving Specht modules and places that theory in a broader context. Finally, we formulate some conjectures involving the theory of stratified algebras and finite Coxeter groups.