In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also...

more general sense, the Poisson bracket is used to define a Poisson algebra, of which the algebra of functions on a Poisson manifold is a special case...

In mathematics, a Poisson superalgebra is a Z2-graded generalization of a Poisson algebra. Specifically, a Poisson superalgebra is an (associative) superalgebra...

{\displaystyle M} , making it into a Lie algebra subject to a Leibniz rule (also known as a Poisson algebra). Poisson structures on manifolds were introduced...

In differential geometry a Poisson supermanifold is a differential supermanifold M such that the supercommutative algebra of smooth functions over it (to...

to finding a (quantum) algebra whose classical limit is a given (classical) algebra such as a Lie algebra or a Poisson algebra. Intuitively, a deformation...

Poisson bracket without resorting to differential equations, see Lie algebra; a Poisson bracket is the name for the Lie bracket in a Poisson algebra....

Baron Siméon Denis Poisson (/pwɑːˈsɒ̃/, US also /ˈpwɑːsɒn/; French: [si.me.ɔ̃ də.ni pwa.sɔ̃]; 21 June 1781 – 25 April 1840) was a French mathematician...

theory as the algebra of generalized Poisson brackets defined on differential forms. A Gerstenhaber algebra is a graded-commutative algebra with a Lie bracket...

deformation quantization of the corresponding Poisson algebra. It is due to Maxim Kontsevich. Given a Poisson algebra (A, {⋅, ⋅}), a deformation quantization...

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...

properties of the non-commutative algebra pass over to corresponding properties of the Poisson algebra. The Poisson bracket must satisfy the identities...

enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal...

differential graded algebra. A Poisson algebra is a commutative associative algebra over a field together with a structure of a Lie algebra so that the Lie...

Octonion algebra Pre-Lie algebra Poisson algebra Process algebra Quadratic algebra Quaternion algebra Rees algebra Relation algebra Relational algebra Rota–Baxter...

bialgebra on a coboundary. They are also called Poisson-Hopf algebras, and are the Lie algebra of a Poisson–Lie group. Lie bialgebras occur naturally in...

Screened Poisson equation Optics Poisson's spot Elasticity Poisson's ratio Dirichlet–Poisson problem Poisson algebra Poisson superalgebra Poisson boundary...

quotient algebra is converted into a Poisson algebra by introducing a Poisson bracket derivable from the action, called the Peierls bracket. This Poisson algebra...

In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with...

mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...

Lie algebra on itself is a representation on an algebra (i.e., acts by derivations on the associative algebra structure), then it is a Poisson algebra. The...

be an "ordinary" product, thus giving rise to the Poisson superalgebra and the Gerstenhaber algebra. Such gradings are also observed in deformation theory...

distributions are the discrete uniform, Bernoulli, binomial, negative binomial, Poisson and geometric distributions. Important continuous distributions include...

mathematical suites are computer algebra systems that use symbolic mathematics. They are designed to solve classical algebra equations and problems in human...

function fields. Algebraic structures occur as both discrete examples and continuous examples. Discrete algebras include: Boolean algebra used in logic gates...

Algebraic structures Algebra of physical space Feynman integral Poisson algebra Quantum group Renormalization group Representation theory Spacetime algebra...

Nambu dynamics. Hamiltonian mechanics Symplectic manifold Poisson manifold Poisson algebra Integrable system Conserved quantity Hamiltonian Fluid Mechanics...

n-algebra Lie operad Particle physics and representation theory Lie superalgebra Orthogonal symmetric Lie algebra Poisson algebra Pre-Lie algebra Quantum...

the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises...

appears, for instance, in an associative algebra structure on a deformation quantization of a Poisson algebra. A microdifferential operator is a type of...