affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra....

answer is that one gets sums of finite-dimensional and affine Lie algebras. The monster Lie algebra satisfies a slightly weaker version of the conditions...

associated to a Lie group (or supergroup), and its symmetry algebra is the affine Lie algebra built from the corresponding Lie algebra (or Lie superalgebra)...

Affine algebra may refer to: Affine Lie algebra, a type of Kac–Moody algebras The Lie algebra of the affine group Finitely-generated algebra Affine Hecke...

Note that every complex Lie algebra can also be viewed as a real Lie algebra of twice the dimension. The Lie algebra of affine transformations of dimension...

quantum affine algebra (or affine quantum group) is a Hopf algebra that is a q-deformation of the universal enveloping algebra of an affine Lie algebra. They...

In mathematics, loop algebras are certain types of Lie algebras, of particular interest in theoretical physics. For a Lie algebra g {\displaystyle {\mathfrak...

the vertex operator algebra. Affine Lie algebra Chiral model Jordan map Virasoro algebra Vertex operator algebra Kac–Moody algebra Goldin 2006 Kac, Victor...

Lie algebra g {\displaystyle {\mathfrak {g}}} is solvable if its derived series terminates in the zero subalgebra. The derived Lie algebra of the Lie...

analogues in the Kac–Moody setting. A class of Kac–Moody algebras called affine Lie algebras is of particular importance in mathematics and theoretical...

(P, η) defines the structure of an affine geometry on M, making it into an affine manifold. The affine Lie algebra aff(n) splits as a semidirect product...

The W(2) algebra coincides with the Virasoro algebra. The W(N) algebra is obtained by Drinfeld-Sokolov reduction of the affine Lie algebra s l ^ N {\displaystyle...

mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket, an...

E_{8},F_{4},G_{2}} ), while affine type indecomposable matrices classify the affine Lie algebras (say over some algebraically closed field of characteristic...

In algebra, a simple Lie algebra is a Lie algebra that is non-abelian and contains no nonzero proper ideals. The classification of real simple Lie algebras...

positive determinant. This is also a Lie group of dimension n 2 {\displaystyle n^{2}} ; it has the same Lie algebra as GL ⁡ ( n , R ) {\displaystyle \operatorname...

This (real) Lie algebra has dimension n2 − 1. More information about the structure of this Lie algebra can be found below in § Lie algebra structure. In...

Dynkin diagrams arise in the classification of semisimple Lie algebras over algebraically closed fields, in the classification of Weyl groups and other...

formula Casimir invariant Killing form Kac–Moody algebra Affine Lie algebra Loop algebra Graded Lie algebra One-parameter group, One-parameter subgroup Matrix...

the Heisenberg Lie algebra with an untwisted affine Kac–Moody Lie algebra (i.e., the universal central extension of the loop algebra on a finite-dimensional...

In mathematics, the special linear Lie algebra of order n {\displaystyle n} over a field F {\displaystyle F} , denoted s l n F {\displaystyle {\mathfrak...

being the use of the corresponding 'infinitesimal' representations of Lie algebras. A complex representation of a group is an action by a group on a finite-dimensional...

In algebraic geometry, an affine variety or affine algebraic variety is a certain kind of algebraic variety that can be described as a subset of an affine...

A, the affine group Aff(A). Similarly, an affine representation of a Lie algebra g on A is a Lie algebra homomorphism from g to the Lie algebra aff(A)...

way as representations of semisimple Lie algebras. Affine Lie algebras are a special case of Kac–Moody algebras, which have particular importance in mathematics...

used to read off the list of simple Lie algebras and Riemannian symmetric spaces. Together with the commutative Lie group of the real numbers, R {\displaystyle...

the field of real and complex numbers. A real Lie algebra g0 is called a real form of a complex Lie algebra g if g is the complexification of g0: g ≃ g...

matrix Lie algebra, there is a linear group (matrix Lie group) with this algebra as its Lie algebra. On the other hand, Lie groups with isomorphic Lie algebras...

ring). *-algebra Affine Lie algebra Akivis algebra Algebra for a monad Albert algebra Alternative algebra AW*-algebra Azumaya algebra Banach algebra Birman–Wenzl...

In the theory of Lie groups, the exponential map is a map from the Lie algebra g {\displaystyle {\mathfrak {g}}} of a Lie group G {\displaystyle G} to...