Affine highest weight categories and affine quasihereditary algebras

作者：Kleshchev Alexander S

来源：Proceedings of the London Mathematical Society, 2015, 110(4): 841-882.

DOI：10.1112/plms/pdv004

Koenig and Xi introduced affine cellular algebras. Kleshchev and Loubert (and Miemietz) showed that an important class of infinite-dimensional algebras, the Khovanov-Lauda-Rouquier algebras R of finite Lie type Gamma, are (graded) affine cellular; in fact, the corresponding affine cell ideals are idempotent. This additional property is reminiscent of the properties of quasihereditary algebras of Cline-Parshall-Scott in a finite-dimensional situation. A fundamental result of Cline-Parshall-Scott says that a finite-dimensional algebra A is quasihereditary if and only if the category of finite-dimensional A-modules is a highest weight category. On the other hand, S. Kato and Brundan-Kleshchev-McNamara proved that the category of finitely generated graded R-modules has many features reminiscent of those of a highest weight category. The goal of this paper is to axiomatize and study the notions of an affine quasihereditary algebra and an affine highest weight category. In particular, we prove an affine analog of the Cline-Parshall-Scott Theorem. We also develop stratified versions of these notions.

• 出版日期2015-4