105 research outputs found
Quivers and matrix equations
No full textAbstractWe discuss methods for solving some familiar matrix equations. The methods were derived from the theory of quivers, a powerful tool in the representation theory of algebras. It is not necessary that the reader understand quivers, but we include a brief explanation for those who may be interested
Quivers com potenciais
No full textIn this thesis we introduce the concepts of potentials in the complete path algebra of a quiver and mutations of quivers with potentials. We study the Jacobian ideal and the Jacobian algebra of a potential, as well as the effect of mutations on the path algebra.Nessa dissertação introduziremos o conceito de potenciais em álgebras de caminhos completas de um quiver e mutação de quivers com potenciais. Estudaremos o ideal Jacobiano e a álgebra Jacobiana de um potencial, bem como o efeito de mutações na álgebra de caminhos
Quivers com potenciais
No full textIn this thesis we introduce the concepts of potentials in the complete path algebra of a quiver and mutations of quivers with potentials. We study the Jacobian ideal and the Jacobian algebra of a potential, as well as the effect of mutations on the path algebra.Nessa dissertação introduziremos o conceito de potenciais em álgebras de caminhos completas de um quiver e mutação de quivers com potenciais. Estudaremos o ideal Jacobiano e a álgebra Jacobiana de um potencial, bem como o efeito de mutações na álgebra de caminhos
Classification of finite type fusion quivers
No full textIn recent work, the second author introduced the concept of Coxeter quivers,
generalizing several previous notions of a quiver representation. Finite type
Coxeter quivers were classified, and their indecomposable objects were shown to
be in bijection with positive roots, generalizing a classical theorem of
Gabriel. In this paper we define fusion quivers, a natural generalization of
Coxeter quivers. We classify the finite type fusion quivers, and prove the
analogue of Gabriel's theorem. As a special case, this proves a generalised
quantum McKay correspondence for fusion categories, an analogue of
Auslander--Reiten's result for finite groups in the fusion categorical setting.Comment: 49 pages. Comments welcomed
Generalised-edged quivers and global forms
No full textNon-simply laced quivers, despite the lack of complete Lagrangian descriptions, play an important role in characterising moduli spaces of supersymmetric field theories. Notably, the moduli space of instantons in non-simply laced gauge groups can be understood by means of such quivers. We generalise the notion of non-simply laced unitary quivers to those whose edges carry two labels (p, q), dubbed (p, q)-edged quivers. The special case of (p, 1) corresponds to a conventional non-simply laced edge studied in the literature. In the case of unframed (p, q)-edged quivers, we show how to parametrise the lattice of magnetic fluxes upon ungauging the decoupled U(1), and how one can pick sublattices thereof corresponding to different global forms of the quiver related by discrete gauging. This form of discrete gauging can be applied to any unframed unitary quivers, not just ones with generalised edges. We utilise both the Hilbert series and the superconformal index to study moduli spaces and ’t Hooft anomalies. In particular, we study mixed ’t Hooft anomalies between a one-form symmetry and a zero-form continuous topological symmetry in various (p, q)-edged quivers. We also provide an alternative realisation of the moduli space of so2n+1 instantons via gauging discrete symmetries in supersymmetric QCD with a symplectic gauge group and a large number of flavours
Four-vertex quivers supporting twisted graded Calabi-Yau algebras
No full textWe study quivers supporting twisted graded Calabi-Yau algebras, building on
work of Rogalski and the first author. Specifically, we classify quivers on
four vertices in which the Nakayama automorphism acts on the degree zero part
by either a four-cycle, a three-cycle, or two two-cycles. In order to realize
algebras associated to some of these quivers, we show that graded twists of a
twisted graded Calabi-Yau algebra is another algebra of the same type.Comment: Some revisions and clarifications adde
Quivers with subadditive labelings: classification and integrability
No full textAbstract
Strictly subadditive, subadditive and weakly subadditive labelings of quivers were introduced by the second author, generalizing Vinberg’s definition for undirected graphs. In our previous work we have shown that quivers with strictly subadditive labelings are exactly the quivers exhibiting Zamolodchikov periodicity. In this paper, we classify all quivers with subadditive labelings. We conjecture them to exhibit a certain form of integrability, namely, as the T-system dynamics proceeds, the values at each vertex satisfy a linear recurrence. Conversely, we show that every quiver integrable in this sense is necessarily one of the 19 items in our classification. For the quivers of type
A
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⊗
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we express the coefficients of the recurrences in terms of the partition functions for domino tilings of a cylinder, called Goncharov–Kenyon Hamiltonians. We also consider tropical T-systems of type
A
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and explain how affine slices exhibit solitonic behavior, i.e. soliton resolution and speed conservation. Throughout, we conjecture how the results in the paper are expected to generalize from
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to all other quivers in our classification
A duality web of linear quivers
No full textAbstractWe show that applying the Bailey lemma to elliptic hypergeometric integrals on the An root system leads to a large web of dualities for N=1 supersymmetric linear quiver theories. The superconformal index of Seiberg's SQCD with SU(Nc) gauge group and SU(Nf)×SU(Nf)×U(1) flavour symmetry is equal to that of Nf−Nc−1 distinct linear quivers. Seiberg duality further enlarges this web by adding new quivers. In particular, both interacting electric and magnetic theories with arbitrary Nc and Nf can be constructed by quivering an s-confining theory with Nf=Nc+1
Algebras whose Auslander-Reiten quivers have large regular components
No full textCrawley-Boevey W, Ringel CM. Algebras whose Auslander-Reiten quivers have large regular components. Journal of Algebra. 1992;153(2):494-516
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