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pro vyhledávání: '"Robert J. Marsh"'
Autor:
Robert J. Marsh, Aslak Bakke Buan
Publikováno v:
International Mathematics Research Notices. 2021:10278-10338
An algebra is said to be $\tau$-tilting finite provided it has only a finite number of $\tau$-rigid objects up to isomorphism. To each such algebra, we associate a category whose objects are the wide subcategories of its category of finite dimensiona
Autor:
Joseph Grant, Robert J. Marsh
Publikováno v:
Pacific Journal of Mathematics. 290:77-116
We describe presentations of braid groups of type ADE and show how these presentations are compatible with mutation of quivers, building on work of Barot and Marsh for Coxeter groups. In types A and D these presentations can be understood geometrical
Publikováno v:
Proceedings of the London Mathematical Society. 113:213-260
We associate a dimer algebra A to a Postnikov diagram D (in a disk) corresponding to a cluster of minors in the cluster structure of the Grassmannian Gr(k,n). We show that A is isomorphic to the endomorphism algebra of a corresponding Cohen-Macaulay
Autor:
Idun Reiten, Robert J. Marsh
Publikováno v:
Mathematische Zeitschrift. 284:643-682
We give an example of a cluster-tilted algebra $$\Lambda $$ with quiver Q, such that the associated cluster algebra $$\mathcal {A}(Q)$$ has a denominator vector which is not the dimension vector of any indecomposable $$\Lambda $$ -module. This answer
Autor:
Konstanze Rietsch, Robert J. Marsh
Publikováno v:
Marsh, R & Rietsch, K 2020, ' The B-model connection and mirror symmetry for Grassmannians ', ADVANCES IN MATHEMATICS, vol. 366, 107027, pp. 1-131 . https://doi.org/10.1016/j.aim.2020.107027
We consider the Grassmannian X = G r n − k ( C n ) and describe a ‘mirror dual’ Landau-Ginzburg model ( X ˇ ∘ , W q : X ˇ ∘ → C ) , where X ˇ ∘ is the complement of a particular anti-canonical divisor in a Langlands dual Grassmannian
Autor:
Robert J. Marsh, Yann Palu
Publikováno v:
Nagoya Mathematical Journal
Nagoya Mathematical Journal, Duke University Press, 2017, 225, pp.64-99. ⟨10.1017/nmj.2016.27⟩
Nagoya Mathematical Journal, Duke University Press, 2017, 225, pp.64-99. ⟨10.1017/nmj.2016.27⟩
If T and T′ are two cluster-tilting objects of an acyclic cluster category related by a mutation, their endomorphism algebras are nearly-Morita equivalent (Buan et al., Cluster-tilted algebras, Trans. Amer. Math. Soc. 359(1) (2007), 323–332 (elec
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::04c17859bb30a64b8ed9f91ed1e0f47e
https://hal.archives-ouvertes.fr/hal-02140340
https://hal.archives-ouvertes.fr/hal-02140340
Autor:
Robert J. Marsh, Yann Palu
Publikováno v:
Proceedings of the London Mathematical Society
Proceedings of the London Mathematical Society, London Mathematical Society, 2014, 108 (2), pp.411-440. ⟨10.1112/plms/pdt032⟩
Proceedings of the London Mathematical Society, London Mathematical Society, 2014, 108 (2), pp.411-440. ⟨10.1112/plms/pdt032⟩
We associate a coloured quiver to a rigid object in a Hom-finite 2-Calabi--Yau triangulated category and to a partial triangulation on a marked (unpunctured) Riemann surface. We show that, in the case where the category is the generalised cluster cat
Autor:
J. S. Scott, Robert J. Marsh
The homogeneous coordinate ring of the Grassmannian Gr k,n has a cluster structure defined in terms of planar diagrams known as Postnikov diagrams. The cluster corresponding to such a diagram consists entirely of Plucker coordinates. We introduce a t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::40fcad5b687f8650409b7a10464c43fe
https://eprints.whiterose.ac.uk/90576/1/marshscottpostprint.pdf
https://eprints.whiterose.ac.uk/90576/1/marshscottpostprint.pdf
Autor:
Aslak Bakke Buan, Robert J. Marsh
Publikováno v:
Journal of Algebra. 323(8):2083-2102
The Fomin-Zelevinsky Laurent phenomenon states that every cluster variable in a cluster algebra can be expressed as a Laurent polynomial in the variables lying in an arbitrary initial cluster. We give representation-theoretic formulas for the denomin
Publikováno v:
Mathematische Zeitschrift. 265:951-970
We generalise the notion of cluster structures from the work of Buan–Iyama–Reiten–Scott to include situations where the endomorphism rings of the clusters may have loops. We show that in a Hom-finite 2-Calabi–Yau category, the set of maximal