By Edward Cline

ISBN-10: 082180488X

ISBN-13: 9780821804889

Feel that $R$ is a finite dimensional algebra and $T$ is a correct $R$-module. enable $A = \textnormal{ End}_R(T)$ be the endomorphism algebra of $T$. This memoir provides a scientific examine of the relationships among the illustration theories of $R$ and $A$, specially these regarding genuine or strength buildings on $A$ which "stratify" its homological algebra. The unique motivation comes from the speculation of Schur algebras and the symmetric crew, Lie idea, and the illustration thought of finite dimensional algebras and finite teams. The e-book synthesizes universal positive factors of some of the above components, and offers a few new instructions. incorporated are an summary "Specht/Weyl module" correspondence, a brand new thought of stratified algebras, and a deformation thought for them. The strategy reconceptualizes many of the modular illustration concept of symmetric teams related to Specht modules and locations that conception in a broader context. eventually, the authors formulate a few conjectures related to the speculation of stratified algebras and finite Coexeter teams, aiming towards realizing the modular illustration thought of finite teams of Lie sort in all features.