Quasi-homomorphisms of quantum cluster algebras

Wen Chang, Min Huang, Jianrong Li

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

In this paper, we study quasi-homomorphisms of quantum cluster algebras, which are quantum analogy of quasi-homomorphisms of cluster algebras introduced by Fraser. For a quantum Grassmannian cluster algebra C q[Gr(k,n)], we show that there is an associated braid group and each generator σ i of the braid group preserves the quasi-commutative relations of quantum Plücker coordinates and exchange relations of the quantum Grassmannian cluster algebra. We conjecture that σ i also preserves r-term (r≥4) quantum Plücker relations of C q[Gr(k,n)] and other relations which cannot be derived from quantum Plücker relations (if any). Up to this conjecture, we show that σ i is a quasi-automorphism of C q[Gr(k,n)] and the braid group acts on C q[Gr(k,n)].

OriginalspracheEnglisch
Seiten (von - bis)506-534
Seitenumfang29
FachzeitschriftJournal of Algebra
Jahrgang638
DOIs
PublikationsstatusVeröffentlicht - 15 Jan. 2024

ÖFOS 2012

  • 101001 Algebra

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