A nonzero 2-cocycle Γ ∈ Z(g,R) on the Lie algebra g of a compact Lie group G defines a twisted version of the Lie-Poisson structure on the dual Lie algebra g∗, leading to a Poisson algebra C∞(g∗(Γ)). Similarly, a multiplier c ∈ Z (G, U(1)) on G which is smooth near the identity defines a twist in the convolution product on G, encoded by the twisted group C∗algebra C∗(G, c). Further to some supe...

‎in this paper lie symmetry analysis is applied in order to find new solutions for fokker plank equation of ornstein-uhlenbeck process‎. ‎this analysis classifies the solutions format of the fokker plank equation by using the lie algebra of the symmetries of our considered stochastic process‎.

The simple 7-dimensional Malcev algebra M is isomorphic to the irreducible sl(2,C)-module V (6) with binary product [x, y] = α(x ∧ y) defined by the sl(2,C)-module morphism α : Λ2V (6)→ V (6). Combining this with the ternary product (x, y, z) = β(x∧y) ·z defined by the sl(2,C)-module morphism β : Λ2V (6)→ V (2) ≈ sl(2,C) gives M the structure of a generalized Lie triple system, or Lie-Yamaguti ...

This paper analyzes the action δ of a Lie algebra X by derivations on a C*–algebra A. This action satisfies an “almost inner” property which ensures affiliation of the generators of the derivations δ with A, and is expressed in terms of corresponding pseudo–resolvents. In particular, for an abelian Lie algebra X acting on a primitive C*–algebra A, it is shown that there is a central extension o...

The notion of vertex operator algebra ([B], [FHL], [FLM]) is the algebraic counterpart of the notion of what is now usually called “chiral algebra” in conformal field theory, and vertex operator algebra theory generalizes the theories of affine Lie algebras, the Virasoro algebra and representations (cf. [B], [DL], [FLM], [FZ]). It has been well known (cf. [FZ], [L1]) that the irreducible highes...

Toroidal Lie algebras are very natural multi-variable generalizations of affine Kac-Moody algebras. The theory of affine Lie algebras is rich and beautiful, having connections with diverse areas of mathematics and physics. Toroidal Lie algebras are also proving themselves to be useful for the applications. Frenkel, Jing and Wang [FJW] used representations of toroidal Lie algebras to construct a...

Let g be a Lie algebra, J an endomorphism of g such that J = −I , and let g be the ieigenspace of J in g := g ⊗R C. When g is a complex subalgebra we say that J is integrable, when g is abelian we say that J is abelian and when g is a complex ideal we say that J is bi-invariant. We note that a complex structure on a Lie algebra cannot be both abelian and biinvariant, unless the Lie bracket is t...

Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie structure together with the Leibniz law. The non-commutative Poisson algebra structures on the infinite-dimensional algebras are studied. We show that these structures are standard on the poset subalgebras of the associative algebra of all endomorphisms of the countable-dimensional vector space T...