Zobrazeno 1 - 10
of 76
pro vyhledávání: '"Gratz, Sira"'
Autor:
Cummings, Charley, Gratz, Sira
Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In particular, f
Externí odkaz:
http://arxiv.org/abs/2407.17369
We show that for a gradable finite dimensional algebra the perfect complexes and bounded derived category cannot be distinguished by homotopy invariants.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/2405.05609
We study a category $\mathcal{C}_2$ of $\mathbb{Z}$-graded MCM modules over the $A_\infty$ curve singularity and demonstrate it has infinite type $A$ cluster combinatorics. In particular, we show that this Frobenius category (or a suitable subcategor
Externí odkaz:
http://arxiv.org/abs/2205.15344
Autor:
Gratz, Sira, Stevenson, Greg
We initiate a systematic study of lattices of thick subcategories for arbitrary essentially small triangulated categories. To this end we give several examples illustrating the various properties these lattices may, or may not, have and show that as
Externí odkaz:
http://arxiv.org/abs/2205.13356
Autor:
Gratz, Sira, Zvonareva, Alexandra
We classify t-structures and thick subcategories in discrete cluster categories $\mathcal{C}(\mathcal{Z})$ of Dynkin type $A$, and show that the set of all t-structures on $\mathcal{C}(\mathcal{Z})$ is a lattice under inclusion of aisles, with meet g
Externí odkaz:
http://arxiv.org/abs/2110.08606
We construct Grassmannian categories of infinite rank, providing an infinite analogue of the Grassmannian cluster categories introduced by Jensen, King, and Su. Each Grassmannian category of infinite rank is given as the category of graded maximal Co
Externí odkaz:
http://arxiv.org/abs/2007.14224
We study cluster tilting modules in mesh algebras of Dynkin type, providing a new proof for their existence. In all but one case, we show that these are precisely the maximal rigid modules, and that they are equivariant for a certain automorphism. We
Externí odkaz:
http://arxiv.org/abs/1904.01369
Publikováno v:
Alg. Number Th. 15 (2021) 29-68
In this article, we construct SL$_k$-friezes using Pl\"ucker coordinates, making use of the cluster structure on the homogeneous coordinate ring of the Grassmannian of $k$-spaces in $n$-space via the Pl\"ucker embedding. When this cluster algebra is
Externí odkaz:
http://arxiv.org/abs/1810.10562
In this survey article we explain the intricate links between Conway-Coxeter friezes and cluster combinatorics. More precisely, we provide a formula, relying solely on the shape of the frieze, describing how each individual entry in the frieze change
Externí odkaz:
http://arxiv.org/abs/1806.06441