is a derivation on the tensor algebra of a manifold. It follows that the adjoint representation of a Lie algebra is a derivation on that algebra. The...

mathematics, differential algebra is, broadly speaking, the area of mathematics consisting in the study of differential equations and differential operators...

extensions of algebraic fields, differential Galois theory studies extensions of differential fields, i.e. fields that are equipped with a derivation, D. Much...

mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology. The term differential is used nonrigorously in calculus...

Look up derivation or derives in Wiktionary, the free dictionary. Derivation may refer to: Morphological derivation, a word-formation process Parse tree...

considered in the context of differential algebra. A differential algebra is an algebra with the extra operation of derivation (algebraic version of differentiation)...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

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

is for R a field and S a unital algebra over R (such as the coordinate ring of an affine variety). Kähler differentials formalize the observation that...

subalgebra of the algebra of linear endomorphisms of A consisting of the derivations. In differential geometry a derivative algebra is a vector space...

Energy Resources ∂, the partial derivative symbol Derivation (differential algebra) on an algebra A over a field K, the space (module) of which is denoted...

of this differential on an exterior algebra makes sense for any Lie algebra, so it is used to define Lie algebra cohomology for all Lie algebras. More generally...

mathematics, a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations...

the chain is either algebraic, logarithmic, or exponential. Suppose F {\displaystyle F} and G {\displaystyle G} are differential fields with Con ⁡ ( F...

U({\mathfrak {g}})} above was that it was a differential algebra, by dint of the fact that any derivation on the Lie algebra can be lifted to U ( g ) {\displaystyle...

operator, contraction, or inner derivation) is a degree −1 (anti)derivation on the exterior algebra of differential forms on a smooth manifold. The interior...

representation theory, mathematical physics, operator algebras, complex analysis, and the theory of partial differential equations. K-theory is an independent discipline...

abstract algebra and topology, a homotopy Lie algebra (or L ∞ {\displaystyle L_{\infty }} -algebra) is a generalisation of the concept of a differential graded...

Algebraic differential geometry may refer to: Differential algebraic geometry Differential geometry of algebraic manifolds Manifolds equipped with a derivation...

calculate BRST cohomology. The differential of this complex is called the Koszul–Tate derivation or Koszul–Tate differential. First suppose for simplicity...

homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra) is an algebraic structure often...

which classical commutative rings are replaced with derived versions such as differential graded algebras, commutative simplicial rings, or commutative ring...

partial differential equations. In differential topology, the exterior derivative and Lie derivative operators have intrinsic meaning. In abstract algebra, the...

again a derivation. This operation makes the space Der k ( A ) {\displaystyle {\text{Der}}_{k}(A)} of all derivations of A over F into a Lie algebra. Informally...

introduced by Robinson (1959). Differentially closed fields are the analogues for differential equations of algebraically closed fields for polynomial equations...

commutative rings, which provide local charts, are replaced by either differential graded algebras (over Q {\displaystyle \mathbb {Q} } ), simplicial commutative...

C^{\infty }(N)} and an arbitrary derivation X ∈ T x M {\displaystyle X\in T_{x}M} at point x ∈ M {\displaystyle x\in M} (a derivation is defined as a linear map...

In mathematics, an algebraic differential equation is a differential equation that can be expressed by means of differential algebra. There are several...

geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is...

In abstract algebra, the Weyl algebras are abstracted from the ring of differential operators with polynomial coefficients. They are named after Hermann...