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Symplectic vector space
About: Symplectic vector space is a research topic. Over the lifetime, 2048 publications have been published within this topic receiving 53456 citations.
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TL;DR: In this article, the authors studied moduli spaces of flat connections on surfaces with boundary, with boundary conditions given by Lagrangian Lie subalgebras, and gave a formula for the symplectic form in terms of holonomies, based on a central extension of the gauge group by closed 2-forms.
Abstract: We study moduli spaces of flat connections on surfaces with boundary, with boundary conditions given by Lagrangian Lie subalgebras The resulting symplectic manifolds are closely related with Poisson-Lie groups and their algebraic structure (such as symplectic groupoid structure) gets a geometrical explanation via 3-dimensional cobordisms We give a formula for the symplectic form in terms of holonomies, based on a central extension of the gauge group by closed 2-forms This construction is finally used for a certain extension of the Morita equivalence of quantum tori to the world of Poisson-Lie groups
16 citations
TL;DR: In this paper, a realization of the Lie algebra of the unitary symplectic group is proposed in terms of boson operators, and the existence of a noncompact orthogonal group, complementary to the symplectic one, is shown.
Abstract: A realization of the Lie algebra of the unitary symplectic group is proposed in terms of boson operators. The existence of a noncompact orthogonal group, complementary to the symplectic one, is shown. The highest weight polynomial of an irreducible representation of the latter group is constructed with the help of the former.
16 citations
TL;DR: In this article, a complex symplectic structure on a Lie algebra h is an integrable complex structure J with a closed non-degenerate ( 2, 0 ) -form.
16 citations
TL;DR: For any n 2 N, there exists a smooth 4-manifold homotopic to a K 3 surface, dened by applying the link surgery method of Fintushel{Stern to a certain 2-component graph link, which admits n inequivalent symplectic structures as mentioned in this paper.
Abstract: In this note we prove that, for any n2 N, there exist a smooth 4{manifold, homotopic to a K3 surface, dened by applying the link surgery method of Fintushel{Stern to a certain 2{component graph link, which admits n inequivalent symplectic structures.
16 citations