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OpenMETU
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Ahmet İrfan Seven
E-mail
aseven@metu.edu.tr
Department
Department of Mathematics
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CLUSTER ALGEBRAS AND SYMMETRIZABLE MATRICES
Seven, Ahmet İrfan (American Mathematical Society (AMS), 2019-07-01)
In the structure theory of cluster algebras, principal coefficients are parametrized by a family of integer vectors, called c-vectors. Each c-vector with respect to an acyclic initial seed is a real root of the correspondi...
REFLECTION GROUP RELATIONS ARISING FROM CLUSTER ALGEBRAS
Seven, Ahmet İrfan (American Mathematical Society (AMS), 2016-11-01)
There is a well-known analogy between cluster algebras and Kac-moody algebras: roughly speaking, Kac-Moody algebras are associated with symmetrizable generalized Cartan matrices while cluster algebras correspond to skew-sy...
CLUSTER ALGEBRAS AND SYMMETRIC MATRICES
Seven, Ahmet İrfan (2015-02-01)
In the structural theory of cluster algebras, a crucial role is played by a family of integer vectors, called c-vectors, which parametrize the coefficients. It has recently been shown that each c-vector with respect to an ...
Maximal green sequences of skew-symmetrizable 3 x 3 matrices
Seven, Ahmet İrfan (2014-01-01)
Maximal green sequences are particular sequences of mutations of skew-symmetrizable matrices which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-Cordova-Vafa in the...
Maximal Green Sequences of Exceptional Finite Mutation Type Quivers
Seven, Ahmet İrfan (2014-01-01)
Maximal green sequences are particular sequences of mutations of quivers which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-Cordova-Vafa in the context of supersym...
Mutation classes of finite type cluster algebras with principal coefficients
Seven, Ahmet İrfan (Elsevier BV, 2013-06-15)
Cluster algebras of finite type is a fundamental class of algebras whose classification is identical to the famous Cartan Killing classification. More recently, Fomin and Zelevinslcy introduced another central notion of cl...
MUTATION CLASSES OF SKEW-SYMMETRIZABLE 3 x 3 MATRICES
Seven, Ahmet İrfan (2013-05-01)
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 stud...
Mutation Classes of 3 x 3 Generalized Cartan Matrices
Seven, Ahmet İrfan (2012-01-01)
One of the recent developments in representation theory has been the introduction of cluster algebras by Fomin and Zelevinsky. It is now well known that these algebras are closely related with different areas of mathematic...
CLUSTER ALGEBRAS AND SEMIPOSITIVE SYMMETRIZABLE MATRICES
Seven, Ahmet İrfan (American Mathematical Society (AMS), 2011-05-01)
There is a particular analogy between combinatorial aspects of cluster algebras and Kac-Moody algebras: roughly speaking, cluster algebras are associated with skew-symmetrizable matrices while Kac-Moody algebras correspond...
Quivers of finite mutation type and skew-symmetric matrices
Seven, Ahmet İrfan (Elsevier BV, 2010-11-01)
Quivers of finite mutation type are certain directed graphs that first arised in Fomin-Zelevinsky's theory of cluster algebras. It has been observed that these quivers are also closely related with different areas of mathe...
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