‎Let $L$ be a Lie algebra‎, ‎$mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$‎. ‎We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields‎. ‎Also‎, ‎we classi...

We develop a complete theory of non-formal deformation quantization on the cotangent bundle weakly exponential Lie group. An appropriate integral formula for star-product is introduced together with suitable space functions which well defined. This becomes Fréchet algebra as pre-C*-algebra. Basic properties are proved, and extension to Hilbert an distributions given. A C*-algebra observables st...

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 ...

Generalized quantum statistics such as para-statistics is usually characterized by certain triple relations. In the case of para-Fermi statistics these relations can be associated with the orthogonal Lie algebra Bn = so(2n + 1); in the case of paraBose statistics they are associated with the Lie superalgebra B(0|n) = osp(1|2n). In a previous paper, a mathematical definition of “a generalized qu...

THEOREM 4. If Q is a Lie algebra of type All then n > 2 and $ SJ' where J is an i.a.a. of second kind in a simple algebra [. Thus a complete classification of Lie algebras of type A,, depends on the classification of simple associative algebras of second kind and of i.a.a.'s relative to cogredience in these algebras. It can be shown that the latter problem is essentially one of ordinary cogredi...

The uniqueness of (the class of) deformation of Poisson Lie algebra po(2n) has long been a completely accepted folklore. Actually this is wrong as stated, because its validity depends on the class of functions that generate po(2n) (e.g., it is true for polynomials but false for Laurent polynomials). We show that, unlike po(2n|m), its quotient modulo center, the Lie superalgebra h(2n|m) of Hamil...

In this paper, we study weight representations over the Schrödinger Lie algebra sn for any positive integer n. It turns out that can be realized by polynomial differential operators. Using realization, give a complete classification of irreducible sn-modules with finite dimensional spaces All such modules clearly characterized tensor product son-modules, sl2-modules and Weyl algebra.