let $mathfrak{l}$ be the virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. we investigate the structure of the lie triplederivation algebra of $mathfrak{l}$ and $mathfrak{g}$. we provethat they are both isomorphic to $mathfrak{l}$, which provides twoexamples of invariance under triple derivation.

in this paper, by using of frobenius theorem a relation between lie subalgebras of the lie algebra of a top space t and lie subgroups of t(as a lie group) is determined. as a result we can consider these spaces by their lie algebras. we show that a top space with the finite number of identity elements is a c^{∞} principal fiber bundle, by this method we can characterize top spaces.

A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

Every affine structure on Lie algebra g defines a representation of g in aff(Rn). If g is a nilpotent Lie algebra provided with a complete affine structure then the corresponding representation is nilpotent. We describe noncomplete affine structures on the filiform Lie algebra Ln. As a consequence we give a nonnilpotent faithful linear representation of the 3-dimensional Heisenberg algebra. 200...

Aslaksen, H., Determining summands in tensor products of Lie algebra representations, Journal of Pure and Applied Algebra 93 (1994) 135-146. We give some results that enable us to find certain summands in tensor products of Lie algebra representations. We concentrate on the splitting of tensor squares into their symmetric and antisymmetric parts. Our results are valid for any Lie algebra of arb...

The PostLie algebra is an enriched structure of the Lie algebra that has recently arisen from operadic study. It is closely related to pre-Lie algebra, Rota-Baxter algebra, dendriform trialgebra, modified classical Yang-Baxter equations and integrable systems. This paper gives a complete classification of PostLie algebra structures on the Lie algebra sl(2,C) up to isomorphism. The classificatio...

some lie algebra analogues of schur's theorem and its converses are presented. as a result, it is shown that for a capable lie algebra l we always have dim l=z(l)  2(dim(l2))2. we also give give some examples sup- porting our results.

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

All Lie bialgebra structures on the Heisenberg–Weyl algebra [A+, A−] = M are classified and explicitly quantized. The complete list of quantum Heisenberg–Weyl algebras so obtained includes new multiparameter deformations, most of them being of the non-coboundary type. A Hopf algebra deformation of a universal enveloping algebra Ug defines in a unique way a Lie bialgebra structure (g, δ) on g [1...

The construction of a class of associative composition algebras qn on R 4 generalizing the wellknown quaternions Q provides an explicit representation of the universal enveloping algebra of the real three-dimensional Lie algebras having tracefree adjoint representations (class A Bianchi type Lie algebras). The identity components of the four-dimensional Lie groups GL(qn,l) Cqn (general linear g...