I review the relationship between AdS/CFT ( anti-de Sitter / conformal field theory) dualities and the general theory of positive energy unitary representations of non-compact space-time groups and supergroups. I show , in particular, how one can go from the manifestly unitary compact basis of the lowest weight ( positive energy) representations of the conformal group ( Wigner picture) to the m...

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

In the paper “Is there a Jordan geometry underlying quantum physics?” [Be08], generalized projective geometries have been proposed as a framework for a geometric formulation of Quantum Theory. In the present note, we refine this proposition by discussing further structural features of Quantum Theory: the link with associative involutive algebras A and with Jordan-Lie and Lie-Jordan algebas. The...

In this paper, we investigate Jordan ?-derivations and Lie on path algebras. This work is motivated by the one of Benkovic done triangular algebras study derivations Li Wei. Namely, main results state that every ?-derivation a standard form algebra when associated quiver acyclic finite.

In this paper, we investigate Jordan ∗-homomorphisms on C∗-algebras associated with the following functional inequality ‖f( b−a 3 ) + f( a−3c 3 ) + f( 3a+3c−b 3 )‖ ≤ ‖f(a)‖. We moreover prove the superstability and the generalized Hyers-Ulam stability of Jordan ∗homomorphisms on C∗-algebras associated with the following functional equation f( b− a 3 ) + f( a− 3c 3 ) + f( 3a+ 3c− b 3 ) = f(a).

We use a generalized Jordan algebra of the second kind to study the recently proposed BLG theory of multiple M2-branes. We find the restriction imposed on the ternary product from its consistency with the BLG theory. [email protected] [email protected] [email protected]

In this paper, left derivations and Jordan left derivations in full and upper triangular matrix rings over unital associative rings are characterized.

Let I be a non-zero left ideal of r-ring M satisfying the condition alpha b beta c= c for all a,b,c, e and alpha, r. We show that contains non-trivial central if is semiprime which admits an appropriate derivations on I, also commutative prime admitting centralizing derivation I. next give some characterizations when generalized act as homomorphisms anti-homomorphisms or two-sided ideals gamma ...