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  • Cluster algebra - Wikipedia
    Cluster algebras are a class of commutative rings introduced by Fomin and Zelevinsky (2002, 2003, 2007) A cluster algebra of rank n is an integral domain A, together with some subsets of size n called clusters whose union generates the algebra A and which satisfy various conditions
  • CLUSTER ALGEBRAS: AN INTRODUCTION - Harvard University
    After giving a detailed example (the type A cluster algebra, and its realization as the coordinate ring of the Grassmannian Gr2,d), we give a more gen-eral definition of cluster algebra, in which both the cluster variables and coefficient variables have their own dynamics
  • Cluster algebras - PNAS
    What Is a Cluster Algebra? Cluster algebras were conceived by Fomin and Zelevinsky (1) in the spring of 2000 as a tool for studying dual canonical bases and total positivity in semisimple Lie groups
  • Cluster algebras I: Foundations
    In this paper, we initiate the study of a new class of algebras, which we call cluster algebras Before giving precise definitions, we present some of the main features of these algebras
  • Cluster Algebras: An Introduction
    Cluster Pattern: an assignment of a labeled seed to each vertex such that the seeds connected by an edge k are related by a mutation in direction k We denote the components of the extended cluster by xt = (x1;t; :::); yt = (y1;t; :::); Bt = (bt ij)
  • Cluster algebra - HandWiki
    Cluster algebras are a class of commutative rings introduced by Fomin and Zelevinsky (2002, 2003, 2007) A cluster algebra of rank n is an integral domain A, together with some subsets of size n called clusters whose union generates the algebra A and which satisfy various conditions
  • Introduction - American Mathematical Society
    se algebras For any positive integer n, a cluster algebra of rank n is a commutative ring with unit and no zero divisors, equipped with a distinguished family of generators called clust
  • [1608. 05735] Introduction to Cluster Algebras. Chapters 1-3
    View a PDF of the paper titled Introduction to Cluster Algebras Chapters 1-3, by Sergey Fomin and 2 other authors
  • Introduction to Cluster Algebras - Brown University
    Cluster algebras are commutative rings with distinguished generators (cluster variables) having a remarkable combinatorial structure The structure of a cluster algebra is encoded by a quiver, and the relations among the cluster variables are encoded by quiver mutation
  • Cluster algebras - PMC
    What Is a Cluster Algebra? Cluster algebras were conceived by Fomin and Zelevinsky (1) in the spring of 2000 as a tool for studying dual canonical bases and total positivity in semisimple Lie groups





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