Jordan Algebras and Their Applications by Kevin Mccrimmon
نویسنده
چکیده
I. Jordan algebras in antiquity (1933-1966). I am unable to prove Jordan algebras were known to Archimedes, or that a complete theory has been found in the unpublished papers of Gauss. Their first appearance in recorded history seems to be in the early 1930's when the theory bursts forth full-grown from the mind, not of Zeus, but of Pascual Jordan, John von Neumann, and Eugene Wigner in their 1934 paper, On an algebraic generalization of the quantum mechanical formalism [14]. In the usual interpretation of quantum mechanics, the observables are Hermitian matrices (or Hermitian operators on Hilbert space) x* = x, where the adjoint x* is the conjugate transpose Jc'. The basic algebraic operations on such observables x are the matrix operations:
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