Geometry of the Moment Map for Representations of Quivers

By W. Crawley‐Boevey. Compositio Mathematica, 2001

335 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/95c23f758396b712e7f8c8073e98eb918e53d919

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Citations in the corpus

Noncommutative geometry and quiver algebras (2005, methodology): “Proof. According to Corollary 5.7 of [ CB1 ], �0 is the set of all nonzero dimension vectors d such that for any nonzero dimension vectors α, β such that α+β = d, one has (α, Aβ) ≤ −2.”
Geometric Construction of Representations of Affine Algebras (2002, background): “In fact, Crawley-Boevey recently proves that M(v) is connected (in fact, he proved it for more general case including varieties discussed in next section) [9].”
Indecomposable parabolic bundles (2004, result): “Compare the theorem also with [ 7, Theorem 3.3 ].”
Almost-commuting variety, D-modules, and Cherednik algebras (2004, methodology): “Using [CB, Lemma 3.4] and [ CB , Lemma 4.1] we find that dim π−1 G(α)� Zreg(β(1), . . . , β(r)) � = |α|2−1+2p(α).”
Symplectic reflection algebras (2007, background): “Since Crawley-Boevey, [38], and Le Bruyn, [103], have described the irreducible Π ′(0,c)(QCM)representations, this then provides an effective combinatorial description of the symplectic leaves of Yc, and in particular of the singular locus of Yc, which by Theorem 4.”
Semicanonical bases and preprojective algebras (2004, neutral): “[12] W. Crawley-Boevey, On the exceptional fibres of Kleinian singularities.”
Rigid modules over preprojective algebras (2005, neutral): “ties of modules over a preprojective algebra correspond to the elements of the canonical basis of a quantum group. These and many other results related to preprojective algebras can be found in [14], [15], [16], [17], [33], [37], [38], [39], [40], for example. 1.2. The aim of this article is twofold”
On cohomological Hall algebras of quivers: Generators (2017, background): “If M(τ) 6= ∅ then the map π restricts to a locally trivial fibration M(τ) → M0(τ) such that, see [8] and [9, cor.”
The Deligne–Simpson problem—a survey (2002, methodology): “The additive version of the DSP is completely solved in [12], for arbitrary eigenvalu uses the results of the earlier papers [13,14] and [15] on preprojective algebras and m map for representations of quivers.”