A geometric model for syzygies over 2-Calabi-Yau tilted algebras II
@inproceedings{Schiffler2021AGM,
title={A geometric model for syzygies over 2-Calabi-Yau tilted algebras II},
author={Ralf Schiffler and Khrystyna Serhiyenko},
year={2021}
}In this article, we continue the study of a certain family of 2-Calabi-Yau tilted algebras, called dimer tree algebras. The terminology comes from the fact that these algebras can also be realized as quotients of dimer algebras on a disc. They are defined by a quiver with potential whose dual graph is a tree, and they are generally of wild representation type. Given such an algebra B, we construct a polygon S with a checkerboard pattern in its interior, that defines a category Diag(S). The…
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One Citation
Cluster Algebra and Representation Theory Programme
- Physics
- 2022
The 3-month programme on Cluster Algebras and Representation Theory at the Isaac Newton Institute in Cambridge has been a very stimulating research experience for the physical and virtual…
References
SHOWING 1-10 OF 43 REFERENCES
Matrix factorizations and singularity categories in codimension two
- MathematicsProceedings of the American Mathematical Society
- 2018
A theorem of Orlov from 2004 states that the homotopy category of matrix factorizations on an affine hypersurface Y is equivalent to a quotient of the bounded derived category of coherent sheaves on…
The Gorenstein-projective modules over a monomial algebra
- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2018
We introduce the notion of a perfect path for a monomial algebra. We classify indecomposable non-projective Gorenstein-projective modules over the given monomial algebra via perfect paths. We apply…
A categorification of Grassmannian cluster algebras
- Mathematics
- 2016
We describe a ring whose category of Cohen–Macaulay modules provides an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of k ‐planes…
Bocklandt, A dimer ABC
- Bull. Lond. Math. Soc
- 2016
Dimer models and cluster categories of Grassmannians
- Mathematics
- 2016
We associate a dimer algebra A to a Postnikov diagram D (in a disc) corresponding to a cluster of minors in the cluster structure of the Grassmannian Gr(k,n) . We show that A is isomorphic to the…
A Geometric Realization of the m-cluster Category of Affine Type A
- Mathematics
- 2015
We give a geometric realization of a subcategory of the m-cluster category 𝒞 m of type , by using (m + 2)-angulations of an annulus with p + q marked points. We also give a bijection between an…
Singularity Categories of some 2-CY-tilted Algebras
- Mathematics
- 2015
We define a class of finite-dimensional Jacobian algebras, which are called (simple) polygon-tree algebras, as a generalization of cluster-tilted algebras of type D$\mathbb {D}$. They are 2-CY-tilted…