The attempt to find out if someone is telling a lie has been of human's interest. One of the techniques which is believed to be efficient in future is fMRI (functional Magnetic Resonance Imaging), using which the changes of regional blood flow during the designed paradigm can be recorded. This method has been considered as a better technique for studying lie and deception. For investigating th...

Let L be a free Lie algebra over a field k, I a non-trivial proper ideal of L, n > 1 an integer. The multiplicator H2(L/I , k) of L/I is not finitely generated, and so in particular, L/I is not finitely presented, even when L/I is finite dimensional.

In this note we study Cartan subalgebras of Lie algebras defined over finite fields. We prove that a possible Lie algebra of minimal dimension without Cartan subalgebras is semisimple. Subsequently, we study Cartan subalgebras of gl(n, F ). AMS classification: 17B50

Some locally finite simple Lie algebras are graded by finite (possibly nonreduced) root systems. Many more algebras are sufficiently close to being root graded that they still can be handled by the techniques from that area. In this paper we single out such Lie algebras, describe them, and suggest some applications of such descriptions.

We study a class of positively graded Lie algebras with a pattern of homogeneous components similar to that of the graded Lie algebra associated to the Nottingham group with respect to its lower central series.

In the present work the properties of Cartan subalgebras and their connection with regular elements in finite dimensional Lie algebras are extended to the case of Leibniz algebras. It is shown that Cartan subalgebras and regular elements of a Leibniz algebra correspond to Cartan subalgebras and regular elements of a Lie algebra by a natural homomorphism. Conjugacy of Cartan subalgebras of Leibn...

1. INTRODUCTION. Some years ago W. Plesken told the first author of a simple but interesting construction of a Lie algebra from a finite group. The authors posed themselves the question as to what the structure of this Lie algebra might be. In particular, for which groups does the construction produce a simple Lie algebra? The answer is given in the present paper; it uses some textbook results ...

The chiral WZNW symplectic form Ω ρ chir is inverted in the general case. Thereby a precise relationship between the arbitrary monodromy dependent 2-form appearing in Ω ρ chir and the exchange r-matrix that governs the Poisson brackets of the group valued chiral fields is established. The exchange r-matrices are shown to satisfy a new dynamical generalization of the classical modified Yang-Baxt...

The symmetry properties of the bosonic string effective action under Poisson-Lie duality transformations are investigated. A convenient and simple formulation of these duality transformations is found, that allows the reduction of the string effective action in a Kaluza-Klein framework. It is shown that the action is invariant provided that the two Lie algebras, forming the Drinfeld double, hav...

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...