Triangulated categories of matrix factorizations for regular systems of weights with $\epsilon=-1$

By H. Kajiura, Kyoji Saito, A. Takahashi. 2007

58 citations recorded by the source corpus.

We construct a full strongly exceptional collection in the triangulated category of graded matrix factorizations of a polynomial associated to a non-degenerate regular system of weights whose smallest exponents are equal to -1. In the associated Grothendieck group, the strongly exceptional collection defines a root basis of a generalized root system of sign (l,0,2) and a Coxeter element of finite order, whose primitive eigenvector is a regular element in the expanded symmetric domain of type IV with respect to the Weyl group.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/62adae6ce9dae6bcc3ccef74ba94f36857230c8a

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Nilpotent operators and weighted projective lines (2010, background): “Stable categories of (graded) Cohen-Macaulay modules play an important role in the analysis of singularities, see [3, 9, 10, 17].”
Weighted Projective Lines Associated to Regular Systems of Weights of Dual Type (2007, background): “in [KST1] for ADE-type and in [ KST2 ] for the case ǫW = −1.”
Extended canonical algebras and Fuchsian singularities (2006, methodology): “first observed by K. Saito and A. Takahashi (personal communication); it is meanwhile published [ 18 ], and uses the technique of matrix factorizations from [17].”