Let Θ be an arbitrary variety of algebras and let Θ0 be the category of all free finitely generated algebras from Θ. We study automorphisms of such categories for special Θ. The cases of the varieties of all groups, all semigroups, all modules over a noetherian ring, all associative and commutative algebras over a field are completely investigated. The cases of associative and Lie algebras are ...

We study the stationary and axisymmetric non-convective differentially rotating perfect-fluid solutions of Einstein’s field equations admitting one conformal symmetry. We analyse the two inequivalent Lie algebras not exhaustively considered in [1] and show that the general solution for each Lie algebra depends on one arbitrary function of one of the coordinates while a set of three ordinary dif...

Space-times admitting an r-parameter Lie group of homotheties are studied for r > 2 devoting a special attention to those representing perfect fluid solutions to Einstein's field equations. 1 Basic facts about homotheties Throughout this paper (M, g) will denote a space-time: M then being a Haus-dorff, simply connected, four-dimensional manifold, and g a Lorentz metric of signature (-,+,+,+). A...

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{...

In this research the relationship between graphitization ability and the carbon equivalent (CE %) of a cast iron have been investigated. The first series of moulds were cast at CE of 3.2% and pouring temperature of 1350°C. The other moulds were cast at different CE% with varying Si content. The graphitization ability( c ) was calculated using the thermodynamics aspects of graphitization and CE%...

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...