Monoidal categorifications of cluster algebras of type A and D
David Hernandez, Bernard Leclerc
TL;DR
This paper introduces monoidal subcategories of quantum affine algebra representations, providing a new representation-theoretic approach to categorify cluster algebras of types A and D.
Contribution
It constructs monoidal categorifications of cluster algebras for types A and D using representation theory of quantum affine algebras, extending previous frameworks.
Findings
Categories provide monoidal categorifications of cluster algebras of types A and D.
The approach is purely representation-theoretical, avoiding geometric methods.
Applicable to linearly oriented Dynkin quivers of types A and D.
Abstract
In this note, we introduce monoidal subcategories of the tensor category of finite-dimensional representations of a simply-laced quantum affine algebra, parametrized by arbitrary Dynkin quivers. For linearly oriented quivers of types A and D, we show that these categories provide monoidal categorifications of cluster algebras of the same type. The proof is purely representation-theoretical, in the spirit of [arXiv:0903.1452].
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology