• Corpus ID: 118325458

Jordan structures in mathematics and physics

@article{Iordanescu2011JordanSI,
  title={Jordan structures in mathematics and physics},
  author={Radu Iordanescu},
  journal={arXiv: Differential Geometry},
  year={2011}
}
  • R. Iordanescu
  • Published 22 June 2011
  • Mathematics
  • arXiv: Differential Geometry
The aim of this paper is to offer an overview of the most important applications of Jordan structures inside mathematics and also to physics, up-dated references being included. For a more detailed treatment of this topic see - especially - the recent book Iordanescu [364w], where sugestions for further developments are given through many open problems, comments and remarks pointed out throughout the text. Nowadays, mathematics becomes more and more nonassociative and my prediction is that in… 

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References

SHOWING 1-10 OF 938 REFERENCES

Soliton equations and differential geometry

In this paper we study certain symplectic, Lie theoretic, and differential geometric properties of soliton equations. The equation for harmonic maps from the Lorentz space R1,1 to a symmetric space,

From Solitons to Knots and Links

Development in the theory of solvable (integrable) models is reviewed. It covers from basic knowledge on completely integrable systems to recent work by the authors. First, soliton theory is briefly

SYMMETRIES OF CERTAIN PHYSICAL THEORIES AND THE JORDAN ALGEBRAS

It is shown that the sequence of Jordan algebras , whose elements are the 3 × 3 Hermitian matrices over the division algebras ℝ, , ℚ and , can be associated with the bosonic string as well as the

Traces On Jordan Algebras

In the theory of Jordan algebras one encounters several definitions of the trace, and it is sometimes unclear whether the different notions are equivalent or not. If we restrict attention to the

On the Structure and Tensor Products of JC-Algebras

Norm closed (or weakly closed) Jordan algebras of self-adjoint operators on a Hilbert space were initially studied by Topping, Effros, and Stormer [15], [4], [12], [13]. These works are very

AN APPLICATION OF THE DIVISION ALGEBRAS, JORDAN ALGEBRAS AND SPLIT COMPOSITION ALGEBRAS

It has been established that the covering group of the Lorentz group in D=3, 4, 6, 10 can be expressed in a unified way, based on the four composition division algebras R, C, Q and O. We discuss, in

Jordan algebras and Capelli identities

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

Statistical Applications of Jordan Algebras

This volume brings together the author's work in mathematical statistics as viewed through the lens of Jordan algebras. The three main areas covered in this work are: applications to random quadratic

Symmetries in science VI : from the rotation group to quantum algebras

Deformable Media with Microstructure T. Ackermann, E. Binz. From Q-Oscillators to Quantum Groups M. Arik. An Analog of the Fourier Transformation for a Q-Harmonic Oscillator R. Askey, et al.

Derivations on Banach-Jordan pairs

A basic continuity problem consists in determining algebraic conditions on a Banach algebra A which ensure that derivations on A are continuous. In 1968, Johnson established the continuity of
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