Mutation classes of skew-symmetrizable $3\times 3$ matrices
نویسندگان
چکیده
منابع مشابه
Mutation Classes of Skew-symmetrizable 3× 3 Matrices
Mutation of skew-symmetrizable matrices is a fundamental operation that first arose in Fomin-Zelevinsky’s theory of cluster algebras; it also appears naturally in many different areas of mathematics. In this paper, we study mutation classes of skew-symmetrizable 3 × 3 matrices and associated graphs. We determine representatives for these classes using a natural minimality condition, generalizin...
متن کاملThe Decomposition Algorithm for Skew-Symmetrizable Exchange Matrices
Some skew-symmetrizable integer exchange matrices are associated to ideal (tagged) triangulations of marked bordered surfaces. These exchange matrices admit unfoldings to skew-symmetric matrices. We develop a combinatorial algorithm that determines if a given skew-symmetrizable matrix is of such type. This algorithm generalizes the one in [1]. As a corollary, we use this algorithm to determine ...
متن کاملCluster Algebras and Semipositive Symmetrizable Matrices
Cluster algebras are a class of commutative rings introduced by Fomin and Zelevinsky. It is well-known that these algebras are closely related with different areas of mathematics. A particular analogy exists between combinatorial aspects of cluster algebras and Kac-Moody algebras: roughly speaking, cluster algebras are associated with skew-symmetrizable matrices while Kac-Moody algebras corresp...
متن کاملQuivers of Finite Mutation Type and Skew-symmetric Matrices
Quivers of finite mutation type have been classified recently in [4]. Main examples of these quivers are the quivers associated with triangulations of surfaces as introduced in [5]. They are also closely related to the representation theory of algebras [1]. In this paper, we study structural properties of finite mutation type quivers. We determine a class of subquivers, which we call basic quiv...
متن کاملOn Some Special Classes of Sonnenschein Matrices
In this paper we consider the special classes of Sonnenschein matrices, namely the Karamata matrices $K[alpha,beta]=left(a_{n,k}right)$ with the entries [{a_{n,k}} = sumlimits_{v = 0}^k {left( begin{array}{l} n\ v end{array} right){{left( {1 - alpha - beta } right)}^v}{alpha ^{n - v}}left( begin{array}{l} n + k - v - 1\ ,,,,,,,,,,k...
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: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2012-11477-7