منابع مشابه
CLUSTER ALGEBRAS AND CLUSTER CATEGORIES
These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...
متن کامل( 2 N ) Algebras And The Corresponding Gauge Field Theories
The extension of the noncommutative u ⋆ (N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism of the star-matrix algebra, we show that the u ⋆ (N) can consistently be restricted to o ⋆ (N) and usp ⋆ (N) algebras that have new mathematical structures. We give explicit fundamental matrix representations of these algebras, through which the...
متن کاملNoncommutative o ⋆ ( N ) and usp ⋆ ( 2 N ) Algebras And The Corresponding Gauge Field Theories
The extension of the noncommutative u ⋆ (N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism of the star-matrix algebra, we show that the u ⋆ (N) can consistently be restricted to o ⋆ (N) and usp ⋆ (N) algebras that have new mathematical structures. We give explicit fundamental matrix representations of these algebras, through which the...
متن کاملcluster algebras and cluster categories
these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...
متن کاملCluster algebras arising from cluster tubes
We study the cluster algebras arising from cluster tubes with rank bigger than 1. Cluster tubes are 2−Calabi-Yau triangulated categories which contain no cluster tilting objects, but maximal rigid objects. Fix a maximal rigid object T in the cluster tube Γn of rank n (n > 1). For any indecomposable rigid object M in Γn, we define an analogous XM of Caldero-Chapton’s formula (or Palu’s cluster c...
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ژورنال
عنوان ژورنال: Progress of Theoretical and Experimental Physics
سال: 2014
ISSN: 2050-3911
DOI: 10.1093/ptep/ptt115