In this paper,we focus on a new lower bound quantum cluster algebra which is generated by the initial quantum cluster variables and the quantum projective cluster variables of an acyclic quantum cluster algebra with p...In this paper,we focus on a new lower bound quantum cluster algebra which is generated by the initial quantum cluster variables and the quantum projective cluster variables of an acyclic quantum cluster algebra with principal coefficients.We show that the new lower bound quantum cluster algebra coincides with the corresponding acyclic quantum cluster algebra.Moreover,we establish a class of formulas between these generators and obtain the dual Poincaré-Birkhoff-Witt(PBW)basis of this algebra.展开更多
We use the quantum version of Chebyshev polynomials to explicitly construct the recursive formulas for the Kronecker quantum cluster algebra with principal coefficients.As a byproduct,we obtain two barinvariant positi...We use the quantum version of Chebyshev polynomials to explicitly construct the recursive formulas for the Kronecker quantum cluster algebra with principal coefficients.As a byproduct,we obtain two barinvariant positive ZP-bases with one being the atomic basis.展开更多
We construct bar-invariant Z[q ±1/2]-bases of the quantum cluster algebra of Kronecker quiver which are quantum analogues of the canonical basis, semicanonical basis and dual semicanonical basis of the correspond...We construct bar-invariant Z[q ±1/2]-bases of the quantum cluster algebra of Kronecker quiver which are quantum analogues of the canonical basis, semicanonical basis and dual semicanonical basis of the corresponding cluster algebra. As a byproduct, we prove positivity of the elements in these bases.展开更多
In this paper, we prove one case of conjecture given by Hemandez and Leclerc. We give a cluster algebra structuure on the Grothendieck ring of a full subcategory of the finite dimensional representations of affine qua...In this paper, we prove one case of conjecture given by Hemandez and Leclerc. We give a cluster algebra structuure on the Grothendieck ring of a full subcategory of the finite dimensional representations of affine quantum group Uq（A3）. As a conclusion, for every exchange relation of cluster algebra, there exists an exact sequence of the full subcategory corresponding to it.展开更多
We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types.Under the specialization of q and coefficients to 1,these bases are generic bases of finite and affine cluster al...We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types.Under the specialization of q and coefficients to 1,these bases are generic bases of finite and affine cluster algebras.展开更多
基金supported by Innovation Research for the Postgraduates of Guangzhou University(Grant No.JCCX2024-053)supported by National Natural Science Foundation of China(Grant No.12371036)+1 种基金supported by National Natural Science Foundation of China(GrantNo.12031007)Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515011739)。
文摘In this paper,we focus on a new lower bound quantum cluster algebra which is generated by the initial quantum cluster variables and the quantum projective cluster variables of an acyclic quantum cluster algebra with principal coefficients.We show that the new lower bound quantum cluster algebra coincides with the corresponding acyclic quantum cluster algebra.Moreover,we establish a class of formulas between these generators and obtain the dual Poincaré-Birkhoff-Witt(PBW)basis of this algebra.
基金supported by National Natural Science Foundation of China(Grant No.11771217)supported by National Natural Science Foundation of China(Grant No.12031007)。
文摘We use the quantum version of Chebyshev polynomials to explicitly construct the recursive formulas for the Kronecker quantum cluster algebra with principal coefficients.As a byproduct,we obtain two barinvariant positive ZP-bases with one being the atomic basis.
基金supported by the Fundamental Research Funds for the Central Universitiespartially supported by the Ph.D. Programs Foundation of Ministry of Education of China (Grant No.200800030058)
文摘We construct bar-invariant Z[q ±1/2]-bases of the quantum cluster algebra of Kronecker quiver which are quantum analogues of the canonical basis, semicanonical basis and dual semicanonical basis of the corresponding cluster algebra. As a byproduct, we prove positivity of the elements in these bases.
基金Project supported by the National Natural Science Foundation of China(Grant No.11475178)
文摘In this paper, we prove one case of conjecture given by Hemandez and Leclerc. We give a cluster algebra structuure on the Grothendieck ring of a full subcategory of the finite dimensional representations of affine quantum group Uq（A3）. As a conclusion, for every exchange relation of cluster algebra, there exists an exact sequence of the full subcategory corresponding to it.
基金supported by the Fundamental Research Funds for the Central UniversitiesNational Natural Science Foudation of China(Grant No.11071133)
文摘We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types.Under the specialization of q and coefficients to 1,these bases are generic bases of finite and affine cluster algebras.
