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30 relations: Associative algebra, Bilinear map, Derivation (differential algebra), Direct sum, Disjoint union, Field (mathematics), Gerstenhaber algebra, Hamiltonian mechanics, Hamiltonian vector field, Jacobi identity, Kontsevich quantization formula, Lie algebra, Lie derivative, Manifold, Mathematics, Moyal bracket, Poisson bracket, Poisson manifold, Poisson superalgebra, Poisson–Lie group, Product rule, Quantum group, Siméon Denis Poisson, Smoothness, Symplectic manifold, Tensor algebra, Universal enveloping algebra, Vector space, Vertex operator algebra, Yvette Kosmann-Schwarzbach.
Associative algebra
In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.
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Bilinear map
In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments.
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Derivation (differential algebra)
In mathematics, a derivation is a function on an algebra which generalizes certain features of the derivative operator.
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Direct sum
The direct sum is an operation from abstract algebra, a branch of mathematics.
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Disjoint union
In set theory, the disjoint union (or discriminated union) of a family of sets is a modified union operation that indexes the elements according to which set they originated in.
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Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
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Gerstenhaber algebra
In mathematics and theoretical physics, a Gerstenhaber algebra (sometimes called an antibracket algebra or braid algebra) is an algebraic structure discovered by Murray Gerstenhaber (1963) that combines the structures of a supercommutative ring and a graded Lie superalgebra.
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Hamiltonian mechanics
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.
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Hamiltonian vector field
In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field, defined for any energy function or Hamiltonian.
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Jacobi identity
In mathematics the Jacobi identity is a property of a binary operation which describes how the order of evaluation (the placement of parentheses in a multiple product) affects the result of the operation.
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Kontsevich quantization formula
In mathematics, the Kontsevich quantization formula describes how to construct a generalized ★-product operator algebra from a given arbitrary Poisson manifold.
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Lie algebra
In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.
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Lie derivative
In differential geometry, the Lie derivative, named after Sophus Lie by Władysław Ślebodziński, evaluates the change of a tensor field (including scalar function, vector field and one-form), along the flow defined by another vector field.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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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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Moyal bracket
In physics, the Moyal bracket is the suitably normalized antisymmetrization of the phase-space star product.
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Poisson bracket
In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system.
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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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Poisson superalgebra
In mathematics, a Poisson superalgebra is a Z2-graded generalization of a Poisson algebra.
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Poisson–Lie group
In mathematics, a Poisson–Lie group is a Poisson manifold that is also a Lie group, with the group multiplication being compatible with the Poisson algebra structure on the manifold.
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Product rule
In calculus, the product rule is a formula used to find the derivatives of products of two or more functions.
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Quantum group
In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebras with additional structure.
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Siméon Denis Poisson
Baron Siméon Denis Poisson FRS FRSE (21 June 1781 – 25 April 1840) was a French mathematician, engineer, and physicist, who made several scientific advances.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Symplectic manifold
In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form, ω, called the symplectic form.
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Tensor algebra
In mathematics, the tensor algebra of a vector space V, denoted T(V) or T(V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product.
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Universal enveloping algebra
In mathematics, a universal enveloping algebra is the most general (unital, associative) algebra that contains all representations of a Lie algebra.
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Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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Vertex operator algebra
In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string theory.
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Yvette Kosmann-Schwarzbach
Yvette Kosmann-Schwarzbach (born 30 April 1941) is a French mathematician and professor.
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References
[1] https://en.wikipedia.org/wiki/Poisson_algebra
