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12 relations: Alan Weinstein, Complex manifold, Complexification, Courant bracket, Differential geometry, Generalized complex structure, Lie algebroid, Lie bialgebroid, Mathematics, Poisson manifold, Quadratic Lie algebra, Theodore James Courant.
Alan Weinstein
Alan David Weinstein (17 June 1943, New York City) is a professor of mathematics at the University of California, Berkeley who works in symplectic geometry, Poisson geometry, and mathematical physics.
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Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.
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Complexification
In mathematics, the complexification of a vector space V over the field of real numbers (a "real vector space") yields a vector space VC over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers.
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Courant bracket
In a field of mathematics known as differential geometry, the Courant bracket is a generalization of the Lie bracket from an operation on the tangent bundle to an operation on the direct sum of the tangent bundle and the vector bundle of ''p''-forms.
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Differential geometry
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.
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Generalized complex structure
In the field of mathematics known as differential geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic structure.
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Lie algebroid
In mathematics, Lie algebroids serve the same role in the theory of Lie groupoids that Lie algebras serve in the theory of Lie groups: reducing global problems to infinitesimal ones.
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Lie bialgebroid
A Lie bialgebroid is a mathematical structure in the area of non-Riemannian differential geometry.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Poisson manifold
In geometry, a Poisson structure on a smooth manifold M is a Lie bracket \ (called a Poisson bracket in this special case) on the algebra (M) of smooth functions on M, subject to the Leibniz rule Said in another manner, it is a Lie algebra structure on the vector space of smooth functions on M such that X_ \stackrel \: (M) \to (M) is a vector field for each smooth function f, which we call the Hamiltonian vector field associated to f. These vector fields span a completely integrable singular foliation, each of whose maximal integral sub-manifolds inherits a symplectic structure.
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Quadratic Lie algebra
A quadratic Lie algebra is a Lie algebra together with a compatible symmetric bilinear form.
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Theodore James Courant
Theodore James "Ted" Courant is an American mathematician who has conducted research in the fields of differential geometry and classical mechanics.
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