Work

Affine cellular algebras and asymptotic algebras

Year: 2026

Type: article

Abstract: The theory of affine cellular algebras A is extended to incorporate their asymptotic algebras A ˆ , clarifying unexpected differences between classical and affine situations and comparing with Lusztig's asymptotic Hecke algebras. The main new results are about a double centraliser property between A and A ˆ , about constructing A ˆ from cell modules of A , about existence of an embedding A → A ˆ and about a faithful functor from torsionless A ˆ -modules to A -modules as well as about the embedding being weakly spectrum preserving (in the sense of Baum and Nistor) and about non-zero endomorphisms of cell modules being injective, while there are no non-zero homomorphisms between non-isomorphic cell modules.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2026.111348

Authors: Paula A.A.B. Carvalho, Steffen Koenig, Christian Lomp

Institutions: Universidade do Porto, University of Stuttgart

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funders: Universidade do Porto, Fundação para a Ciência e a Tecnologia, Centro de Matemática Universidade do Porto