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Quivers of finite mutation type and skew-symmetric matrices

โœ Scribed by Ahmet I. Seven

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
339 KB
Volume
433
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

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 mathematics. In fact, main examples of finite mutation type quivers are the quivers associated with triangulations of surfaces. In this paper, we study structural properties of finite mutation type quivers in relation with the corresponding skew-symmetric matrices. We obtain a characterization of finite mutation type quivers that are associated with triangulations of surfaces and give a new numerical invariant for their mutation classes.

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Determinant and Pfaffian of sum of skew
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โœ Tin-Yau Tam; Mary Clair Thompson ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 177 KB

We completely describe the determinants of the sum of orbits of two real skew symmetric matrices, under similarity action of orthogonal group and the special orthogonal group, respectively. We also study the Pfaffian case and the complex case.