Ring theoretical properties of affine cellular algebras

• Type: Article in International Scientific Journal
• Date: 2017

Authors

Paula A.A.B. Carvalho (Author) FCUP; Koenig, S (Author) Other; Christian Lomp (Author) FCUP; Shalile, A (Author) Other

Journal

Title: Journal of Algebra

Vol. 476

Pages: 494-518

ISSN: 0021-8693

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 1 Citation

Scientific classification

CORDIS: Physical sciences > Mathematics ; Physical sciences > Mathematics > Algebra

Other information

Authenticus ID: P-00M-B2E

DOI: 10.1016/j.jalgebra.2016.12.016

Abstract (EN): As a generalisation of Graham and Lehrer's cellular algebras, affine cellular algebras have been introduced in [12] in order to treat affine Hecke algebras of type A and affine versions of diagram algebras like affine Temperley Lieb algebras in a unifying fashion. Affine cellular algebras include Kleshchev's graded quasihereditary algebras, Khovanov Lauda Rouquier algebras and various other classes of algebras. In this paper we will study ring theoretical properties of affine cellular algebras. We show that any affine cellular algebra A satisfies a polynomial identity. Furthermore, we show that A can be embedded into its asymptotic algebra if the occurring commutative affine k-algebras B-j are reduced and the determinants of the swich matrices are non-zero divisors. As a consequence, we show that the Gelfand-Kirillov dimension of A is less than or equal to the largest Krull dimension of the algebras B-j and that equality holds, in case all affine cell ideals are idempotent or if the Krull dimension of the algebras B-j is less than or equal to 1. Special emphasis is given to the question when an affine cell ideal is idempotent, generated by an idempotent or finitely generated.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 25