in this paper, a useful classification of all lie subalgebras of a given lie algebraup to an inner automorphism is presented. this method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. after main results, we have applied this procedure for classifying the lie subalgebras of some examples of lie al...

Using tensor categories, we present new constructions of several the exceptional simple Lie superalgebras with integer Cartan matrix in characteristic $p = 3$ and 5$ from complete classification modular indecomposable their subquotients over algebraically closed fields by Bouarroudj, Grozman, Leites 2009. Specifically, let $\mathbf{\alpha}_p$ denote kernel Frobenius endomorphism on additive gro...

motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎it is shown‎ ‎that every lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎the definition of lie $n$-higher‎ ‎derivations on operator algebras and related pote...

assume that $(n,l)$, is a pair of finite dimensional nilpotent lie algebras, in which $l$ is non-abelian and $n$ is an ideal in $l$ and also $mathcal{m}(n,l)$ is the schur multiplier of the pair $(n,l)$. motivated by characterization of the pairs $(n,l)$ of finite dimensional nilpotent lie algebras by their schur multipliers (arabyani, et al. 2014) we prove some properties of a pair of nilpoten...

In this paper, a useful classification of all Lie subalgebras of a given Lie algebraup to an inner automorphism is presented. This method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. After main results, we have applied this procedure for classifying the Lie subalgebras of some examples of Lie al...

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 ...

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.

The 3.0-A-resolution x-ray structure of rat liver 3 alpha-hydroxysteroid dehydrogenase/dihydrodiol dehydrogenase (3 alpha-HSD, EC 1.1.1.50) was determined by molecular replacement using human placental aldose reductase as the search model. The protein folds into an alpha/beta or triose-phosphate isomerase barrel and lacks a canonical Rossmann fold for binding pyridine nucleotide. The structure ...