In this paper we prove that in prime characteristic there is a functor −p-Leib from the category of diassociative algebras to the category of restricted Leibniz algebras, generalizing the functor from associative algebras to restricted Lie algebras. Moreover we define the notion of restricted universal enveloping diassociative algebra Udp(g) of a restricted Leibniz algebra g and we show that Ud...

Compactification can control chaotic Mixmaster behavior in gravitational systems with p–form matter: we consider this in light of the connection between supergravity models and Kac–Moody algebras. We show that different compactifications define “mutations” of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems ...

For any affine Weyl group, we introduce the pre-canonical bases. They are a set of bases {Ni}1?i?m+1 (where m is height highest root) spherical Hecke algebra that interpolates between standard basis N1 and canonical Nm+1. The expansion Ni+1 in terms Ni many cases very simple conjecture type A it positive.

using the hyers-ulam-rassias stability method, weinvestigate isomorphisms in banach algebras and derivations onbanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}moreover, we prove the hyers-ulam-rassias stability of homomorphismsin banach algebras and of derivations on banach ...

Our purpose in this paper is the generalization of notions quadratic and symplectic structures to case 3-(Hom)-$\rho$-Lie algebras. We describe some properties them by expressing related lemmas theorems. Also, we introduce concept 3-pre-(Hom)-$\rho$-Lie algebras define their representation.

The short-line match-cast joint method of pre-casting concrete segments has proved to be the most versatile and reliable way to building pre-cast segmental bridges. The essential feature of match casting is that successive segments are cast against adjoining segment in the correct relative orientation with each other starting from the first segment away from the pier. The segments are subsequen...