Quiver varieties and Lusztig's algebra

By A. Malkin, V. Ostrik, M. Vybornov. 2004

56 citations recorded by the source corpus.

Abstract We study preprojective algebras of graphs and their relationship to module categories over representations of quantum SL ( 2 ) . As an application, ADE quiver varieties of Nakajima are shown to be subvarieties of the variety of representations of a certain associative algebra introduced by Lusztig.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1199097193c76843632eff0b15fc7d96f6f999f6

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On cohomological Hall algebras of quivers: Generators (2017, background): “QC Q/C t(2) Id/ (1), where Q is the adjacency matrix of Q, see [14, 23].”
Calabi-Yau algebras (2006, unknown): “structure given by convolution; the monoidal structure is given by the formula E⊗E′ = L i,k∈I(E⊗E ′) i,k,where (E⊗E′)i,k := M j∈I (E i,j⊗E′ j,k), ∀E= L i,j∈IEi,j,E ′ = L i,j∈IE ′ ∈CI-bimod. Following [MOV], we also consider the category Fun(CI,CI), of all additive functors CI →CI. The category Fun(C”
Calabi-Yau Frobenius algebras (2007, methodology): “Q, whose entries are (Hη Q)ij = tr(ηeiAej), where I ¯η := {i∈I: ¯η(i) = i}. These matrices were computed in the D,E cases in [Eu07c]. In fact, HQitself was originally computed for all Dynkin cases in [MOV06]: since Ais free over k, HQ= h(A;1) is the Hilbert series matrix h(A;t) evaluated at t= 1. In”
Calabi–Yau triangulated categories (2008, background): “4.3] following notes by B. Crawley-Boevey and in [ 45 ] for general quivers).”
Quantum Groups and Quantum Cohomology (2012, background): “otents e i, iPI, namely paths of zero length that start and end at a vertex i. We set PathpQ dq ij e iPathpQ dqe j; 130 131 6.1 The core Yangian and similarly for pQ dq. It is known, see for example [72, 30], that character pQ dq ij C 1 ji ~ 1 b C 1 ij ; (6.5) provided Qis not a quiver of ADE type.”