‎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...

Suppose $pi:mathcal{A}rightarrow mathcal{B}$ is a surjective unital $ast$-homomorphism between C*-algebras $mathcal{A}$ and $mathcal{B}$, and $0leq aleq1$ with $ain  mathcal{A}$. We give a sufficient condition that ensures there is a proection $pin mathcal{A}$ such that $pi left( pright) =pi left( aright) $. An easy consequence is a result of [L. G. Brown and G. k. Pedersen, C*-algebras of real...

in this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and also investigate the hyers-ulam-rassiasstability of n-jordan *-homomorphisms on c*-algebras.

The structure constants for Moyal brackets of an infinite basis of functions on the algebraic manifolds M of pseudo-unitary groups U (N + , N −) are provided. They generalize the Virasoro and W ∞ algebras to higher dimensions. The connection with volume-preserving diffeomorphisms on M , higher generalized-spin and tensor operator algebras of U (N + , N −) is discussed. These centrally-extended,...

We study exceptional torsion in the integral cohomology of a family of p-groups associated to p-adic Lie algebras. A spectral sequence E r [g] is defined for any Lie algebra g which models the Bockstein spectral sequence of the corresponding group in characteristic p. This spectral sequence is then studied for complex semisimple Lie algebras like sln(C), and the results there are transferred to...

We show that every groupoid C*-algebra is isomorphic to its opposite, and deduce there exist C*-algebras are not stably C*-algebras, though many of them twisted C*-algebras. also prove the opposite algebra a section Fell bundle over natural bundle.

The theory of Lie algebras has many applications in mathematics and physics. One possible way of generalizing the theory of Lie algebras is to develop the theory of Lie-like algebras algebras, where the notion of a Lie-like algebras algebra was introduced in [4]. One of Lie’s Theorems claims that the only irreducible representations of a solvable Lie algebra over an algebraically closed field k...

in this paper we study the properties of derivations of a b, where a and b are simple separable c*-algebras, and a b is the c*-completion of a b with respect to a c*-norm yon a b and we will characterize the derivations of a b in terms of the derivations of a and b

Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article is written based on the author’s seminar talks on nongraded infinite-dimensional simple Lie algebras. The key constructional ingredients of our Lie algebras ...

Orthogonal decompositions (OD:s) that are monomial have been constructed for most simple Lie algebras but in some cases the existence of an OD is still an open question. One of them is Lie algebras of type Cn where n is not a power of 2. In this paper we use computational methods to prove that C3 has no monomial OD. 1 Orthogonal decompositions of simple Lie algebras The basic question, of which...