Results 1 to 10 of about 24,636 (184)
The rank of a quiver representation
Journal of Algebra, 2008 We define a functor which gives the "global rank of a quiver representation" and prove that it has nice properties which make it a generalization of the rank of a linear map. We demonstrate how to construct other "rank functors" for a quiver Q, which induce ring homomorphisms (called "rank functions") from the representation ring of Q to Z.
Ryan Kinser
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Big Finitistic Dimensions for Categories of Quiver Representations [PDF]
Mathematics Interdisciplinary Research, 2021 Assume that A is a Grothendieck category and R is the category of all A-representations of a given quiver Q. If Q is left rooted and A has a projective generator, we prove that the big finitistic flat (resp. projective) dimension FFD(A) (resp. FPD(A)) of
Roghayeh Bagherian, Esmaeil Hosseini
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The Representation Theory of Neural Networks
Mathematics, 2021 In this work, we show that neural networks can be represented via the mathematical theory of quiver representations. More specifically, we prove that a neural network is a quiver representation with activation functions, a mathematical object that we ...
Marco Armenta, Pierre-Marc Jodoin
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Unitarizable Representations of Quivers [PDF]
Algebras and Representation Theory, 2012 27 pages, Section 2.3 reorganized, final version, to appear in Algebras and Representation ...
Weist, Thorsten, Yusenko, Kostyantyn
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The combinatorics of quiver representations [PDF]
Annales de l'Institut Fourier, 2011 We give a description of faces, of all codimensions, for the cones spanned by the set of weights associated to the rings of semi-invariants of quivers. For a triple flag quiver and its faces of codimension 1 this description reduces to the result of Knutson-Tao-Woodward on the facets of the Klyachko cone.
Derksen, Harm, Weyman, Jerzy
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BPS states meet generalized cohomology
Journal of High Energy Physics, 2023 In this note we review a construction of a BPS Hilbert space in an effective supersymmetric quiver theory with 4 supercharges. We argue abstractly that this space contains elements of an equivariant generalized cohomology theory E G ∗ − $$ {E}_G^{\ast ...
Dmitry Galakhov
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Representations of thread quivers [PDF]
Proceedings of the London Mathematical Society, 2013 We introduce thread quivers as an (infinite) generalization of quivers, and show that every k-linear (k algebraically closed) hereditary category with Serre duality and enough projectives is equivalent to the category of finitely presented representations of a thread quiver.
Berg, C., van Roosmalen, A.
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Quivers and the Euclidean algebra (Extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We show that the category of representations of the Euclidean group $E(2)$ is equivalent to the category of representations of the preprojective algebra of the quiver of type $A_{\infty}$. Furthermore, we consider the moduli space of $E(2)$-modules along
Alistair Savage
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Semisimple representations of quivers [PDF]
Transactions of the American Mathematical Society, 1990 We discuss the invariant theory of the variety of representations of a quiver and present generators and relations.
Lieven Le Bruyn, Claudio Procesi
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Sequential deconfinement in 3d N $$ \mathcal{N} $$ = 2 gauge theories
Journal of High Energy Physics, 2021 We consider 3d N $$ \mathcal{N} $$ = 2 gauge theories with fundamental matter plus a single field in a rank-2 representation. Using iteratively a process of “deconfinement” of the rank-2 field, we produce a sequence of Seiberg-dual quiver theories.
Sergio Benvenuti +2 more
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