Non-commutative Symplectic Geometry, Quiver varieties, and Operads

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dc.creatorGinzburg, Victor
dc.date2000-05-17
dc.date2000-06-02
dc.date.accessioned2026-07-07T04:35:19Z
dc.date.available2026-07-07T04:35:19Z
dc.descriptionQuiver varieties have recently appeared in various different areas of Mathematics such as representation theory of Kac-Moody algebras and quantum groups, instantons on 4-manifolds, and resolutions Kleinian singularities. In this paper, we show that many important affine quiver varieties, e.g., the Calogero-Moser space, can be imbedded as coadjoint orbits in the dual of an appropriate infinite dimensional Lie algebra. In particular, there is an infinitesimally transitive action of the Lie algebra in question on the quiver variety. Our construction is based on an extension of Kontsevich's formalism of `non-commutative Symplectic geometry'. We show that this formalism acquires its most adequate and natural formulation in the much more general framework of P-geometry, a `non-commutative geometry' for an algebra over an arbitrary cyclic Koszul operad.
dc.descriptionminor corrections made; LaTeX2e, 20 pages
dc.identifierhttps://arxiv.org/abs/math/0005165
dc.identifierhttp://arxiv.org/abs/math/0005165
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59213
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectAlgebraic Geometry
dc.subjectK-Theory and Homology
dc.titleNon-commutative Symplectic Geometry, Quiver varieties, and Operads
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