In differential geometry, a Lie-algebra-valued form is a differential form with values in a Lie algebra. Such forms have important applications in the...

generally, the exterior algebra can be defined for modules over a commutative ring. In particular, the algebra of differential forms in k {\displaystyle k}...

on the algebra of real-valued differentiable functions on Rn. The Lie derivative with respect to a vector field is an R-derivation on the algebra of differentiable...

In differential geometry, the Lie derivative (/liː/ LEE), named after Sophus Lie by Władysław Ślebodziński, evaluates the change of a tensor field (including...

(\omega )\cdot \phi ,} where, following the notation in Lie algebra-valued differential form § Operations, we wrote ( ρ ( ω ) ⋅ ϕ ) ( v 1 , … , v k +...

such theories is the curvature form of the connection, which is represented in a gauge by a Lie algebra-valued one-form A. The Yang–Mills field F is then...

important case of vector-valued differential forms are Lie algebra-valued forms. (A connection form is an example of such a form.) Let M be a smooth manifold...

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

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

exterior algebra of the Lie algebra, with a suitable differential. The construction of this differential on an exterior algebra makes sense for any Lie algebra...

affine Lie algebra, one can also form the associated affine Kac-Moody algebra, as described below. From a purely mathematical point of view, affine Lie algebras...

denotes the differential of Lg) on a Lie group is a Lie algebra under the Lie bracket of vector fields. Any tangent vector at the identity of a Lie group can...

In mathematics, Lie group–Lie algebra correspondence allows one to correspond a Lie group to a Lie algebra or vice versa, and study the conditions for...

In mathematics, the Maurer–Cartan form for a Lie group G is a distinguished differential one-form on G that carries the basic infinitesimal information...

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...

like an algebra over a field. Algebra over an operad Alternative algebra Clifford algebra Composition algebra Differential algebra Free algebra Geometric...

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...

{\displaystyle [\cdot \wedge \cdot ]} is defined in the article "Lie algebra-valued form" and D denotes the exterior covariant derivative. In other terms...

Galois groups in differential Galois theory tend to be matrix Lie groups, as compared with the finite groups often encountered in algebraic Galois theory...

Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and...

matrix multiplication). The algebraic objects amenable to such a description include groups, associative algebras and Lie algebras. The most prominent of these...

Lie algebroid can thus be thought of as a "many-object generalisation" of a Lie algebra. Lie algebroids play a similar same role in the theory of Lie...

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

Multilinear algebra is the study of functions with multiple vector-valued arguments, with the functions being linear maps with respect to each argument...

representation theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory. Operator algebras can be used to study...

important role. A Lie group is a group in the category of smooth manifolds. Beside the algebraic properties this enjoys also differential geometric properties...

calculus and differential geometry, such as an infinitesimal change in the value of a function Differential algebra Differential calculus Differential of a function...

of view, an automorphic form over the group G(AF), for an algebraic group G and an algebraic number field F, is a complex-valued function on G(AF) that...

an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulae for solutions of partial differential equations...

consists of differential p-forms on a manifold M, is a differential graded algebra. A Poisson algebra is a commutative associative algebra over a field...