Compare triangular bases of acyclic quantum cluster algebras
نویسندگان
چکیده
منابع مشابه
Triangular Bases in Quantum Cluster Algebras
A lot of recent activity has been directed toward various constructions of “natural” bases in cluster algebras. We develop a new approach to this problem which is close in spirit to Lusztig’s construction of a canonical basis, and the pioneering construction of the Kazhdan–Lusztig basis in a Hecke algebra. The key ingredient of our approach is a new version of Lusztig’s Lemma that we apply to a...
متن کاملAcyclic Quantum Cluster Algebras
This thesis concerns quantum cluster algebras. For skew-symmetric acyclic quantum cluster algebras, we express the quantum F -polynomials and the quantum cluster monomials in terms of Serre polynomials of quiver Grassmannians of rigid modules. Then we introduce a new family of graded quiver varieties together with a new t-deformation, and generalize Nakajima’s t-analogue of q-characters to thes...
متن کاملPreprojective cluster variables of acyclic cluster algebras
It is proved that any cluster-tilted algebra defined in the cluster category C(H) has the same representation type as the initial hereditary algebra H . For any valued quiver (Γ,Ω), an injection from the subset PI(Ω) of the cluster category C(Ω) consisting of indecomposable preprojective objects, preinjective objects and the first shifts of indecomposable projective modules to the set of cluste...
متن کاملA Quantum Analogue of Generic Bases for Affine Cluster Algebras
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.
متن کاملGreedy bases in rank 2 quantum cluster algebras.
We identify a quantum lift of the greedy basis for rank 2 coefficient-free cluster algebras. Our main result is that our construction does not depend on the choice of initial cluster, that it builds all cluster monomials, and that it produces bar-invariant elements. We also present several conjectures related to this quantum greedy basis and the triangular basis of Berenstein and Zelevinsky.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2018
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/7610