Generalized Jordan-Wigner transformations.

Linear Canonical Transformations and Quantum Phase: A unified canonical and algebraic approach

The algebra of generalized linear quantum canonical transformations is examined in the perspective of Schwinger’s unitary-canonical operator basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and in particular with the generalized quantum action-angle phase space formalism is established and it is shown that the conceptual foundation of the qu...

Dualities and the Unitary Representations of Non - compact Groups and Supergroups : Wigner versus Dirac

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...

On p-semilinear transformations

In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...

On Jordan left derivations and generalized Jordan left derivations of matrix rings

Abstract. Let R be a 2-torsion free ring with identity. In this paper, first we prove that any Jordan left derivation (hence, any left derivation) on the full matrix ringMn(R) (n 2) is identically zero, and any generalized left derivation on this ring is a right centralizer. Next, we show that if R is also a prime ring and n 1, then any Jordan left derivation on the ring Tn(R) of all n×n uppe...

On Jordan generalized k-derivations of semiprime Γ_N-Rings