منابع مشابه
Algorithms and Properties for Positive Symmetrizable Matrices
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating symmetrizable matrices with specific characteristics, called positive quasi-Cartan companion matrices. Here, symmetrizable matrix are those which are symmetric when m...
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 کاملMutation 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 کاملCluster Algebras of Finite Type and Positive Symmetrizable Matrices
The paper is motivated by an analogy between cluster algebras and Kac-Moody algebras: both theories share the same classification of finite type objects by familiar Cartan-Killing types. However the underlying combinatorics beyond the two classifications is different: roughly speaking, Kac-Moody algebras are associated with (symmetrizable) Cartan matrices, while cluster algebras correspond to s...
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 ...
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1959
ISSN: 0003-4851
DOI: 10.1214/aoms/1177706367