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...

Vector fields whose flow preserves a symplectic form up to a constant, such as simple mechanical systems with friction, are called “conformal”. We develop a reduction theory for symmetric conformal Hamiltonian systems, analogous to symplectic reduction theory. This entire theory extends naturally to Poisson systems: given a symmetric conformal Poisson vector field, we show that it induces two r...

‎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...

In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by 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{...

This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations...

To the Editor, The Indian Medical Gazette StR,?I have read with considerable interest your leading article on epidemic dropsy in the October issue of the Gazette. I wish to draw your attention to one or two points in connection with your reference to our work on the subject. While offering criticism on the deductions made by us from our experiments you make no mention of the fact that albumin w...