2023/03/23 by Wen-Chang Chang, Min Huang, Chang, Wen +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Braid #Braid group #Cluster algebra #Combinatorics #Commutative property #Conjecture #FOS: Mathematics #Generator (circuit theory) #Grassmannian #Group (periodic table) #Homomorphism #Mathematics #Physics #Pure mathematics #Quantum #Quantum Algebra (math.QA) #Quantum mechanics
paper · pdf · doi:10.48550/arxiv.2303.13030
openalex publication_date 2023/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℂq[\rm Gr(k,n)], we show that there is an associated braid group and each generator σi 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 σi also preserves r-term (r ≥ 4) quantum Plücker relations of ℂq[\rm Gr(k,n)] and other relations which cannot be derived from quantum quantum Plücker relations (if any). Up to this conjecture, we show that σi is a quasi-automorphism of ℂq[\rm Gr(k,n)] and the braid group acts on ℂq[\rm Gr(k,n)].