We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the Minkowskian spacetimes by an extra ”dilatonic” coordinate, whose rotation, Lorentz and conformal groups are SO(d−1), SO(d−1, 1)×SO(1, 1) and SO(d, 2)×SO(2, 1), respective...

We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the Minkowskian spacetimes by an extra “dilatonic” coordinate, whose rotation, Lorentz and conformal groups are SO(d−1), SO(d−1, 1)×SO(1, 1) and SO(d, 2)×SO(2, 1), respective...

We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the Minkowskian spacetimes by an extra “dilatonic” coordinate, whose rotation, Lorentz and conformal groups are SO(d−1), SO(d−1, 1)×SO(1, 1) and SO(d, 2)×SO(2, 1), respective...

Let m ≥ 0, n ≥ 0 be fixed integers with m + n 6= 0 and let R be a ring. It is our aim in this paper to investigate additive mapping T : R → R satisfying the relation (m + n)T (x2) = mT (x)x + nxT (x) for all x ∈ R. This research is a continuation of our earlier work ([11]). Throughout, R will represent an associative ring with center Z(R). Given an integer n ≥ 2, a ring R is said to be n−torsio...

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

Let $ {\mathcal{A}} be a unital \ast -algebra containing nontrivial projection. Under some mild conditions on , it is shown that map \Phi:{\mathcal{A}}\rightarrow{\mathcal{A}} nonlinear mixed Jordan triple * -derivation if and only \Phi an additive -derivation. In particular, we apply the above result to prime -algebras, von Neumann algebras with no central summands of type I_{1} factor algebra...

In this article, it is proved that under some conditions every bijective Jordan triple product homomorphism from generalized matrix algebras onto rings is additive. As a corollary, we obtain that every bijective Jordan triple product homomorphism from Mn(A) (A is not necessarily a prime algebra) onto an arbitrary ring R is additive.