Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Quasi-Cartan companions of elliptic cluster algebras
Download
index.pdf
Date
2016
Author
Velioğlu, Kutlucan
Metadata
Show full item record
Item Usage Stats
100
views
29
downloads
Cite This
There is an analogy between combinatorial aspects of cluster algebras and diagrams corresponding to skew-symmetrizable matrices. In this thesis, we study quasi-Cartan companions of skew-symmetric matrices in the mutation-class of exceptional elliptic diagrams. In particular, we establish the existence of semipositive admissible quasi-Cartan companions for these matrices and exhibit some other invariant properties.
Subject Keywords
Cluster algebras.
,
Elliptic functions.
URI
http://etd.lib.metu.edu.tr/upload/12620006/index.pdf
https://hdl.handle.net/11511/25662
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
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 study mutation classes of skew-symmetrizable 3 x 3 matrices and associated graphs. We determine representatives for these classes using a natural minimality condition, generalizing and strengthening results of Beineke-BrustleHille and Felikson-Shapiro-Tumarkin. Furthermore, we obtain a new num...
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 acyclic initial seed is a real root of the corresponding root system. In this paper, we obtain an interpretation of this result in terms of symmetric matrices. We show that for skew-symmetric cluster algebras, the c-vectors associated with any seed defines a quasi-Cartan companion for the ...
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 to (symmetrizable) generalized Cartan matrices. Both classes of algebras and the associated matrices have the same classification of finite type objects by the well-known Cartan-Killing types. In this paper, we study an extension of this correspondence to the affine type. In particular, w...
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 corresponding root system, and the c-vectors associated with any seed defines a symmetrizable quasi-Cartan companion for the corresponding exchange matrix. We establish basic combinatorial properties of these companions. In particular, we show that c-vectors define an admissible cut of edges in the a...
Electromagnetic target recognition with the fused MUSIC spectrum matrix method: Applications and performance analysis for incomplete frequency data
Secmen, Mustafa; Ekmekci, Evren; Sayan, Gönül (2007-01-01)
The aim of this paper is to apply an electromagnetic target recognition method, which is based on the use of fused MUSIC spectrum matrices, to the case of incomplete frequency domain data. The aforementioned method was suggested recently and succesfully applied to both canonical and complicated targets in the presence of complete frequency domain data [1]. However, most of the real world applications involve the use of severely incomplete frequency data, especially missing low frequency information. In this...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
K. Velioğlu, “Quasi-Cartan companions of elliptic cluster algebras,” Ph.D. - Doctoral Program, Middle East Technical University, 2016.