scholarly journals Dihedral $G$-Hilb via representations of the McKay quiver

2012 ◽  
Vol 88 (5) ◽  
pp. 78-83 ◽  
Author(s):  
Alvaro Nolla de Celis
Keyword(s):  
Mckay Quiver

scholarly journals CONNECTIVITY PROPERTIES OF MCKAY QUIVERS

2020 ◽  
pp. 1-13
Author(s):  
HAZEL BROWNE
Keyword(s):  
Finite Groups ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Self Duality ◽  
Finite Dimensional ◽  
Representations Of Finite Groups ◽  
Necessary And Sufficient ◽  
Mckay Quiver

Abstract We present several results on the connectivity of McKay quivers of finite-dimensional complex representations of finite groups, with no restriction on the faithfulness or self-duality of the representations. We give examples of McKay quivers, as well as quivers that cannot arise as McKay quivers, and discuss a necessary and sufficient condition for two finite groups to share a connected McKay quiver.

scholarly journals Moduli of McKay quiver representations II: Gröbner basis techniques

2007 ◽  
Vol 316 (2) ◽  
pp. 514-535 ◽  
Author(s):  
Alastair Craw ◽  
Diane Maclagan ◽  
Rekha R. Thomas
Keyword(s):  
Gröbner Basis ◽  
Quiver Representations ◽  
Grobner Basis ◽  
Mckay Quiver

scholarly journals Danilov's resolution and representations of the McKay quiver

2014 ◽  
Vol 66 (3) ◽  
pp. 355-375 ◽  
Author(s):  
Oskar Kędzierski
Keyword(s):  
Mckay Quiver

scholarly journals McKay Quivers and Lusztig Algebras of Some Finite Groups

2021 ◽  
Author(s):  
Ragnar-Olaf Buchweitz ◽  
Eleonore Faber ◽  
Colin Ingalls ◽  
Matthew Lewis
Keyword(s):  
Finite Groups ◽  
Group Rings ◽  
Young Diagrams ◽  
Reflection Groups ◽  
Conceptual Approach ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Morita Equivalent ◽  
Skew Group Rings ◽  
Mckay Quiver

AbstractWe are interested in the McKay quiver Γ(G) and skew group rings A ∗G, where G is a finite subgroup of GL(V ), where V is a finite dimensional vector space over a field K, and A is a K −G-algebra. These skew group rings appear in Auslander’s version of the McKay correspondence. In the first part of this paper we consider complex reflection groups $\mathsf {G} \subseteq \text {GL}(V)$ G ⊆ GL ( V ) and find a combinatorial method, making use of Young diagrams, to construct the McKay quivers for the groups G(r,p,n). We first look at the case G(1,1,n), which is isomorphic to the symmetric group Sn, followed by G(r,1,n) for r > 1. Then, using Clifford theory, we can determine the McKay quiver for any G(r,p,n) and thus for all finite irreducible complex reflection groups up to finitely many exceptions. In the second part of the paper we consider a more conceptual approach to McKay quivers of arbitrary finite groups: we define the Lusztig algebra $\widetilde {A}(\mathsf {G})$ A ~ ( G ) of a finite group $\mathsf {G} \subseteq \text {GL}(V)$ G ⊆ GL ( V ) , which is Morita equivalent to the skew group ring A ∗G. This description gives us an embedding of the basic algebra Morita equivalent to A ∗ G into a matrix algebra over A.

scholarly journals Moduli of McKay quiver representations I: the coherent component

2007 ◽  
Vol 95 (1) ◽  
pp. 179-198 ◽  
Author(s):  
Alastair Craw ◽  
Diane Maclagan ◽  
Rekha R. Thomas
Keyword(s):  
Quiver Representations ◽  
Coherent Component ◽  
Mckay Quiver
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