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Stratifying Endomorphism Algebras
     

Stratifying Endomorphism Algebras

by Leonard Scott, Edward Cline, Brian Parshall
 

ISBN-10: 082180488X

ISBN-13: 9780821804889

Pub. Date: 12/09/1996

Publisher: American Mathematical Society

Suppose that $R$ is a finite dimensional algebra and $T$ is a right $R$-module. Let $A = \mathrm{ End}_R(T)$ be the endomorphism algebra of $T$. This memoir presents a systematic study of the relationships between the representation theories of $R$ and $A$, especially those involving actual or potential structures on $A$ which ''stratify'' its homological algebra.

Overview

Suppose that $R$ is a finite dimensional algebra and $T$ is a right $R$-module. Let $A = \mathrm{ End}_R(T)$ be the endomorphism algebra of $T$. This memoir presents a systematic study of the relationships between the representation theories of $R$ and $A$, especially those involving actual or potential structures on $A$ which ''stratify'' its homological algebra. The original motivation comes from the theory of Schur algebras and the symmetric group, Lie theory, and the representation theory of finite dimensional algebras and finite groups. The book synthesizes common features of many of the above areas, and presents a number of new directions. Included are an abstract ''Specht/Weyl module'' correspondence, a new theory of stratified algebras, and a deformation theory for them. The approach reconceptualizes most of the modular representation theory of symmetric groups involving Specht modules and places that theory in a broader context. Finally, the authors formulate some conjectures involving the theory of stratified algebras and finite Coexeter groups, aiming toward understanding the modular representation theory of finite groups of Lie type in all characteristics.

Product Details

ISBN-13:
9780821804889
Publisher:
American Mathematical Society
Publication date:
12/09/1996
Series:
Memoirs of the American Mathematical Society Series , #124
Pages:
119

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