It was proved by Jacobson [2] that every finite-dimensional Lie algebra of characteristic p has a finite-dimensional representation space which is not semisimple. In this note we prove a similar result for Jacobson's restricted Lie algebras [l]. The structure of a restricted Lie algebra L over a field F of characteristic p comprises, in addition to the ordinary Lie algebra structure, a map x—*-...

We look for the approximation of exp(A1 + A2) by a product in form exp(x1A1) exp(y1A2) · · · exp(xnA1) exp(ynA2). We specially are interested in minimal approximations, with respect to the number of terms. After having shown some isomorphisms between specific free Lie subalgebras, we will prove the equivalence of the search of such approximations and approximations of exp(A1 + · · ·+ An). The m...

using fixed point method, we prove some new stability results for lie $(alpha,beta,gamma)$-derivations and lie $c^{ast}$-algebra homomorphisms on lie $c^{ast}$-algebras associated with the euler-lagrange type additive functional equation begin{align*} sum^{n}_{j=1}f{bigg(-r_{j}x_{j}+sum_{1leq i leq n, ineq j}r_{i}x_{i}bigg)}+2sum^{n}_{i=1}r_{i}f(x_{i})=nf{bigg(sum^{n}_{i=1}r_{i}x_{i}bigg)} end{...

The main point of the construction of spin Calogero type classical integrable systems based on dynamical r-matrices, developed by L.-C. Li and P. Xu, is reviewed. It is shown that non-Abelian dynamical r-matrices with variables in a reductive Lie algebra F and their Abelian counterparts with variables in a Cartan subalgebra of F lead essentially to the same models.

It is an initially surprising fact how much of the geometry and arithmetic of Shimura varieties (e.g., moduli spaces of abelian varieties) is governed by the theory of linear algebraic groups. This is in some sense unfortunate, because the theory of algebraic groups (even over the complex numbers, and still more over a nonalgebraically closed field like Q) is rich and complicated, containing fo...

In the current study, we report on an experiment examining whether functional magnetic resonance imaging (fMRI) lie detection evidence would influence potential jurors' assessment of guilt in a criminal trial. Potential jurors (N = 330) read a vignette summarizing a trial, with some versions of the vignette including lie detection evidence indicating that the defendant was lying about having co...

Let G be a connected and reductive group over the algebraically closed field K. J-P. Serre has introduced the notion of a G-completely reducible subgroup H ≤ G. In this note, we give a notion of G-complete reducibility – G-cr for short – for Lie subalgebras of Lie(G), and we show that if the smooth subgroup H < G is G-cr, then Lie(H) is G-cr as well.

We show that O(2, 2) transformation of SU(2) WZNW model gives rise to marginal deformation of this model by the operator d 2 zJ(z) ¯ J (¯ z) where J, ¯ J are U(1) currents in the Cartan subalgebra. Generalization of this result to other WZNW theories is discussed. We also consider O(3, 3) transformation of the product of an SU(2) WZNW model and a gauged SU(2) WZNW model. The three parameter set...

Abstract. The underlying field is of characteristic p > 2. In this paper, we first use the method of computing the homogeneous derivations to determine the first cohomology of the so-called odd contact Lie algebra with coefficients in the even part of the generalized Witt Lie superalgebra. In particular, we give a generating set for the Lie algebra under consideration. Finally, as an applicatio...