# Download A Taste of Jordan Algebras (Universitext) eBook

## by **Kevin McCrimmon**

The book describes the history of Jordan algebras, and describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov.

The book describes the history of Jordan algebras, and describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov. To keep the exposition elementary, the structure theory is developed for linear Jordan algebras (where the scalar ring contains 1/2, avoiding the nuisancy distractions of characteristic 2), though the modern quadratic methods are used throughout.

A taste of Jordan algebras, Kevin McCrimmon

A taste of Jordan algebras, Kevin McCrimmon. p. cm. - (Universitext). This book tells the story of one aspect of Jordan structure theory: the origin of the theory in an attempt by quantum physicists to nd algebraic systems more general than hermitian matrices, and ending with the surpris-ing proof by Em Zel’manov that there is really only one such system, the 27-dimensional Albert algebra, much too small to accommodate quantum.

In this book, Kevin McCrimmon describes the history of Jordan Algebras and he describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov. To keep the exposition elementary, the structure theory is developed for linear Jordan algebras, though the modern quadratic methods are used throughout. Both the quadratic methods and the Zelmanov results go beyond the previous textbooks on Jordan theory, written in the 1960's and 1980's before the theory reached its final form.

Kevin McCrimmon introduced the concept of a quadratic Jordan algebra and developed a structure theory of Jordan algebras over an arbitrary ring of scalars. Библиографические данные. A Taste of Jordan Algebras.

Kevin Mor McCrimmon (born September 1941) is an American mathematician, specializing in Jordan algebras. He is known for his introduction of quadratic Jordan algebras in 1966. McCrimmon attended secondary school in Champaign-Urbana, Illinois and then received his bachelor's degree in mathematics in 1960 from Reed College in Portland, Oregon. from Yale University in 1965 with thesis Norms and Noncommutative Jordan Algebras supervised by Nathan Jacobson.

On several occasions I and colleagues have found ourselves teaching a o- semester course for students at the second year of graduate study in ma- ematics who want to gain a general perspective on Jordan algebras, their structure, and their role in mathematics, or want to gain direct experience with nonassociative algebra.

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A Taste of Jordan Algebras by Kevin McCrimmon. On p. 70 of Mathematical Foundations of Quantum Mechanics, by none other than George W. Mackey, one of the grand-masters of unitary representation theory (and much else besides), there occurs the following sequence. Whenever A + B is always defined we can define 'symmetrized products' of bounded observables by setting.

A Taste of Jordan Algebras (Universitext).

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A Taste of Jordan Algebras. Article · January 2003 with 21 Reads.

A Taste of Jordan Algebras. How we measure 'reads'. Good surveys on Euclidean Jordan algebras can be found in books such as A Taste of Jordan Algebras of Kevin McCrimmon, Analysis on Symmetric Cones of Faraut and Korányi and in the Koecher's Minnesota Notes on Jor- dan Algebras and Their Applications. Euclidean Jordan algebras become a good tool for the analysis of primal dual interior point.

This book describes the history of Jordan algebras and describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov. Jordan algebras crop up in many surprising settings, and find application to a variety of mathematical areas. No knowledge is required beyond standard first-year graduate algebra courses.