in this paper, we classify the indecomposable non-nilpotent solvable lie algebras with $n(r_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $n(r_n,m,r)$.we also prove that these solvable lie algebras are complete and unique, up to isomorphism.

We construct, by model-theoretic methods, several exponentiations on the universal enveloping algebra U of the Lie algebra sl2(C). MSC: 16S30, 17B10, 03C60.

2 Virasoro as a local Lie algebra on C 3 2.1 Dolbeault resolution of holomorphic vector fields . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Lie algebra extensions and the cocycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.1 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.2 A cocycle for LC . . . . . ....

It is shown that every abelian regular Lie group is a quotient of its Lie algebra via the exponential mapping. This paper is a sequel of [3], see also [4], chapter VIII, where a regular Lie group is defined as a smooth Lie group modeled on convenient vector spaces such that the right logarithmic derivative has a smooth inverse Evol : C(R, g) → C(R, G), the canonical evolution operator, where g ...

This is an entirely expository piece: the main results discussed are very wellknown and the approach we take is not really new, although the presentation may be somewhat different to what is in the literature. The author’s main motivation for writing this piece comes from a feeling that the ideas deserve to be more widely known. Let g be a Lie algebra over R or C. . A vector subspace I ⊂ g is a...

In this dissertation, we investigate the cohomology theory of restricted Lie algebras. Motivations for the definition of a restricted Lie algebra are given and the theory of ordinary Lie algebra cohomology is briefly reviewed, including a discussion on algebraic interpretations of the low dimensional cohomology spaces of ordinary Lie algebras. The general Cartan-Eilenberg construction of the st...

‎in this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎we show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a lie groupoid‎. ‎using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the lie algebra of all vector fields on the smooth...

We extend a Lie algebra expansion method recently introduced for the (2 + 1)dimensional kinematical algebras to the expansions of the (3 + 1)-dimensional Galilei algebra. One of these expansions goes from the (3 + 1)-dimensional Galilei algebra to the Poincaré one; this process introduces a curvature equal to −1/c, where c is the relativistic constant, in the space of worldlines. This expansion...

We study the C∗-algebra An,θ generated by the Anzai flow on the n-dimensional torus T. It is proved that this algebra is a simple quotient of the group C∗-algebra of a lattice subgroup Dn of a (n + 2)-dimensional connected simply connected nilpotent Lie group Fn whose corresponding Lie algebra is the generic filiform Lie algebra fn. Other simple infinite dimensional quotients of C∗(Dn) are also...

It is known that a family of transfer matrix functional equations, the T-system, can be compactly written in terms of the Cartan matrix of a simple Lie algebra. We formally replace this Cartan matrix of a simple Lie algebra with that of an affine Lie algebra, and then we obtain a system of functional equations different from the T-system. It may be viewed as an X (a) n type affine Toda field eq...