Finite dimensional algebras and highest weight categories. (English) Zbl 0657.18005

Cline, E.; Parshall, B.; Scott, L.

J. Reine Angew. Math. 391, 85-99 (1988).

The concept of highest weight categories is defined. It is shown that the theory of highest weight categories is related to the theory of quasi- hereditary algebras. The results relating these theories appear to provide a strong link between the representation theory of finite dimensional algebras and that of semisimple groups and Lie algebras.

Reviewer: C.Năstăsescu

MSC:

18E30	Derived categories, triangulated categories (MSC2010)
17B10	Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
20G05	Representation theory for linear algebraic groups
16Gxx	Representation theory of associative rings and algebras
16P10	Finite rings and finite-dimensional associative algebras

Keywords:

highest weight categories; quasi-hereditary algebras; representation theory of finite dimensional algebras; semisimple groups; Lie algebras