Triangulated categories of singularities and equivalences between Landau-Ginzburg models

Orlov, Dmitri

doi:10.1070/sm2006v197n12abeh003824

Cited by 405 publications

(708 citation statements)

References 28 publications

(73 reference statements)

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“…finitely generated projective) Z-graded R-modules. This category was considered by Buchweitz [7] and Orlov [30,31]. It was shown in [26] that there exists a tilting object T in the triangulated category Der Z sing (R) whose endomorphism ring is isomorphic to an extended canonical algebra C[P ].…”

Section: N=0mentioning

confidence: 99%

Algebras Whose Coxeter Polynomials are Products of Cyclotomic Polynomials

Peña

2013

Algebr Represent Theor

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Abstract. Let A be a finite dimensional algebra over an algebraically closed field k. Assume A is basic connected with n pairwise non-isomorphic simple modules. We consider the Coxeter transformation φ A as the automorphism of the Grothendieck group K 0 (A) induced by the Auslander-Reiten translation τ in the derived category Der(modA) of the module category modA of finite dimensional left A-modules. We say that A is an algebra of cyclotomic type if the characteristic polynomial χ A of φ A is a product of cyclotomic polynomials. There are many examples of algebras of cyclotomic type in the representaton theory literature: hereditary algebras of Dynkin and extended Dynkin types, canonical algebras, some supercanonical and extended canonical algebras. Among other results, we show that: (a) algebras satisfying the fractional Calabi-Yau property have periodic Coxeter transformation and are, therefore, of cyclotomic type, and (b) algebras whose homological form h A is non-negative are of cyclotomic type. For an algebra A of cyclotomic type we describe the shape of the Auslander-Reiten components of Der(modA).

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Section: N=0mentioning

confidence: 99%

Algebras Whose Coxeter Polynomials are Products of Cyclotomic Polynomials

Peña

2013

Algebr Represent Theor

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“…For us it is important to note that in the category of matrix factorizations of topological B-banes, in addition to the gauge equivalences (2.2), two matrix factorizations are also equivalent if they only differ by blocks of trivial matrix factorizations [37,15,38] …”

Section: Jhep02(2007)006mentioning

confidence: 99%

“…All those described ingredients are captured in a graded category [37,38,26,39,22], where the objects are matrix factorizations, the morphisms between objects are open-string states, and finally the shift functor is the operator, T . For us it is important to note that in the category of matrix factorizations of topological B-banes, in addition to the gauge equivalences (2.2), two matrix factorizations are also equivalent if they only differ by blocks of trivial matrix factorizations [37,15,38] …”

Section: Jhep02(2007)006mentioning

confidence: 99%

D-brane monodromies from a matrix-factorization perspective

Jockers

2007

J. High Energy Phys.

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“…Orlov then shows that DGrB(W ) is equivalent to D gr Sg (A) introduced in [23] which is defined as follows. Let gr-A be the category of graded A-modules.…”

Section: Gr Sg (A)mentioning

confidence: 99%

Landau-Ginzburg to Calabi-Yau dictionary for D-branes

Aspinwall¹

2007

Journal of Mathematical Physics

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Based on work by Orlov, we give a precise recipe for mapping between B-type D-branes in a Landau-Ginzburg orbifold model (or Gepner model) and the corresponding large-radius Calabi-Yau manifold. The D-branes in Landau-Ginzburg theories correspond to matrix factorizations and the D-branes on the Calabi-Yau manifolds are objects in the derived category. We give several examples including branes on quotient singularities associated to weighted projective spaces. We are able to confirm several conjectures and statements in the literature.

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Triangulated categories of singularities and equivalences between Landau-Ginzburg models

Cited by 405 publications

References 28 publications

Algebras Whose Coxeter Polynomials are Products of Cyclotomic Polynomials

Algebras Whose Coxeter Polynomials are Products of Cyclotomic Polynomials

D-brane monodromies from a matrix-factorization perspective

Landau-Ginzburg to Calabi-Yau dictionary for D-branes

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