We define skew matrix gamma ring and describe the constitution of Jordan left centralizers derivations on a -ring. also show properties these concepts.

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...

A basic result in Intuitionism is Π2-Conservativity. Take any proof p in Classical Arithmetic of some Π2-statement (some arithmetical statement ∀x.∃y.P (x, y), with P decidable). Then we may effectively turn p in some intuitionistic proof of the same statement. In a previous paper [1], we generalized this result: any classical proof p of an arithmetical statement ∀x.∃y.P (x, y), with P of degre...

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...

We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let A be a Banach algebra and X a Banach A-module, f : X → X and g : A → A. The mappings Δ1 f,g , Δ2 f,g , Δ3 f,g , and Δ4 f,g are defined and it is proved that if ‖Δ1 f,g x, y, z,w ‖ resp., ‖Δ3 f,g x, y, z,w, α, β ‖ is dominated by φ x, y, z,w , then f is a generalized re...

The purpose of this paper is to establish a connection between semisimple Jordan algebras and certain invariant differential operators on symmetric spaces; and to prove an identity for such operators which generalizes the classical Capelli identity. The norm function on a simple real Jordan algebra gives rise to invariant differential operators Dm on a certain symmetric space which is a natural...

Let K,S,D be a division ring an endomorphism and a S-derivation of K, respectively. In this setting we introduce generalized noncommutative symmetric functions and obtain Viète formula and decompositions of differential operators. W -polynomials show up naturally, their connections with P -independency, Vandermonde and Wronskian matrices are briefly studied. The different linear factorizations ...

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.

We construct a closed Jordan curve γ ⊂ R so that γ∩S is uncountable whenever S is a line segment whose endpoints are contained in different connected components of R \ γ. We say that a Jordan arc σ ⊂ R crosses a compact set K ⊂ R if the two endpoints of σ are in different connected components of R \ K. Clearly any arc crossing K must intersect K in at least one point of K. If the intersection c...

In this paper, we define new families of Generalized Fibonacci polynomials and Lucas develop some elegant properties these families. We also find the relationships between family generalized k-Fibonacci known polynomials. Furthermore, generalizations in matrix representation. Then establish Cassini’s Identities for their Finally, suggest avenues further research.