Zobrazeno 1 - 10
of 10
pro vyhledávání: '"Sira Gratz"'
Publikováno v:
Journal of the London Mathematical Society.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d9b1b9a1d4788bd46cbd33103218152d
https://doi.org/10.1112/jlms.12735
https://doi.org/10.1112/jlms.12735
Publikováno v:
International Mathematics Research Notices
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9d9b03e8a0648723322858ea047a8dc4
https://doi.org/10.1093/imrn/rnad004
https://doi.org/10.1093/imrn/rnad004
Publikováno v:
Linear Algebra and its Applications. 630:112-157
We study cluster tilting modules in mesh algebras of Dynkin type as defined in [12] , providing a new proof for their existence. Except for type G 2 , we show that these are precisely the maximal rigid modules, and that they are equivariant for a cer
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2b1c6b3db038fe1630a1f15fcbd9f995
https://doi.org/10.1016/j.laa.2021.07.021
https://doi.org/10.1016/j.laa.2021.07.021
Publikováno v:
Baur, K, Faber, E, Gratz, S, Serhiyenko, K & Todorov, G 2018, ' Friezes satisfying higher SL$_k$-determinants ', Alg. Number Th. https://doi.org/10.2140/ant.2021.15.29
Gratz, S H, Baur, K, Faber, E, Serhiyenko, K & Todorov, G 2021, ' Friezes satisfying higher SLk-determinants. ', Algebra and Number Theory, vol. 15, no. 1 .
Gratz, S H, Baur, K, Faber, E, Serhiyenko, K & Todorov, G 2021, ' Friezes satisfying higher SLk-determinants. ', Algebra and Number Theory, vol. 15, no. 1 .
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ea2d4390144fc2a66792b153073fc576
https://eprints.whiterose.ac.uk/163712/8/ant-v15-n1-p02-s.pdf
https://eprints.whiterose.ac.uk/163712/8/ant-v15-n1-p02-s.pdf
Publikováno v:
Association for Women in Mathematics Series ISBN: 9783319986838
In this survey chapter, 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 cha
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f52cfe07767e6908ec4e141c1e16cc2f
https://doi.org/10.1007/978-3-319-98684-5_4
https://doi.org/10.1007/978-3-319-98684-5_4
Autor:
Sira Gratz
Publikováno v:
Gratz, S 2013, ' Mutation of torsion pairs in cluster categories of Dynkin type $D$ ', Applied Categorical Structures, . https://doi.org/10.1007/s10485-014-9387-2
Mutation of torsion pairs in triangulated categories and its combinatorial interpretation for the cluster category of Dynkin type $A_n$ and of type $A_\infty$ have been studied by Zhou and Zhu. In this paper we present a combinatorial model for mutat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f0b799e57c3b8b5b631bf44526789b55
https://doi.org/10.1007/s10485-014-9387-2
https://doi.org/10.1007/s10485-014-9387-2
We give a combinatorial classification of cluster tilting subcategories and torsion pairs in Igusa--Todorov cluster categories of Dynkin type $A_{ \infty }$.
This is the final accepted version, which will appear in Mathematische Zeitschrift. 25
This is the final accepted version, which will appear in Mathematische Zeitschrift. 25
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bdd79a442cdd86b45aa03edc679dc438
http://arxiv.org/abs/1711.07528
http://arxiv.org/abs/1711.07528
Autor:
Karin Baur, Sira Gratz
We introduce mutation along infinite admissible sequences for infinitely marked surfaces, that is surfaces with infinitely many marked points on the boundary. We show that mutation along such admissible sequences produces a preorder on the set of tri
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dbefe3b3e133447acc60a9c5a587ea25
Autor:
Jan E. Grabowski, Sira Gratz
We provide a graded and quantum version of the category of rooted cluster algebras introduced by Assem, Dupont and Schiffler and show that every graded quantum cluster algebra of infinite rank can be written as a colimit of graded quantum cluster alg
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::331c6a7b9b9c139acafa810d11e94143
Autor:
Sira Gratz
Publikováno v:
Gratz, S 2014, ' Cluster algebras of infinite rank as colimits ', Mathematische Zeitschrift, . https://doi.org/10.1007/s00209-015-1524-6
We formalize the way in which one can think about cluster algebras of infinite rank by showing that every rooted cluster algebra of infinite rank can be written as a colimit of rooted cluster algebras of finite rank. Relying on the proof of the posiv
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::49fc90e29982102685f459157a41839b
https://pure.au.dk/ws/files/281555979/1410.5374v2.pdf
https://pure.au.dk/ws/files/281555979/1410.5374v2.pdf