Ebook: Nathan Jacobson Collected Mathematical Papers: Volume 2 (1947–1965)

This collection contains all my published papers, both research and expository, that were published from 1934 to 1988. The research papers arranged in chronological order appear in Volume I and II and in the first part of Volume III. The expository papers, which are mainly reports presented at conferences, appear in chronological order in the last part of Volume III. Volume I covers the period 1910 to 1947, the year I moved to Yale, Volume II covers the period 1947 to 1965 when I became Chairman of the Department at Yale and Volume III covers the period from 1965 to 1989, which goes beyond my assumption of an emeritus status in 1981. I have divided the time interval covered in each volume into subintervals preceded by an account of my personal history during this period, and a commentary on the research papers published in the period. I have omitted commentaries on the expository papers and have sorted out the commentaries on the research papers according to the principal fields of my research. The personal history has been based on my recollections, checked against written documentation in my file of letters as well as diaries. One of these was a diary I kept of my trip to the USSR in 1961; the others were diaries Florie (Florence) kept during other major visits abroad. I have also consulted Professor A. W. Tucker on historical details on Princeton during the 1930's.

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Content:
Front Matter....Pages i-xviii
A Personal History and Commentary....Pages 1-16
Lie and Jordan Triple Systems....Pages 17-38
Classification and Representation of Semi-Simple Jordan Algebras....Pages 39-67
Derivation Algebras and Multiplication Algebras of Semi-Simple Jordan Algebras....Pages 68-76
Enveloping Algebras of Semi-Simple Lie Algebras....Pages 77-86
Some Remarks on One-Sided Inverses....Pages 88-91
Jordan Homomorphisms of Rings....Pages 93-116
Completely Reducible Lie Algebras of Linear Transformations....Pages 117-125
General Representation Theory of Jordan Algebras....Pages 127-148
Homomorphisms of Jordan Rings of Self-Adjoint Elements....Pages 149-151
Operator Commutativity in Jordan algebras....Pages 152-164
A Kronecker Factorization Theorem for Cayley Algebras and the Exceptional Simple Jordan Algebra....Pages 165-167
Structure of Alternative and Jordan Bimodules....Pages 169-172
A Note on Automorphisms and Derivations of Lie Algebras....Pages 173-178
Commutative Restricted Lie Algebras....Pages 179-249
A Note on Two Dimensional Division Ring Extensions....Pages 251-253
A Personal History and Commentary....Pages 254-259
A Theorem on the Structure of Jordan Algebras....Pages 261-267
Generation of separable and central simple algebras....Pages 269-288
On Reduced Exceptional Simple Jordan Algebras....Pages 290-297
On Jordan Algebras with Two Generators....Pages 299-309
Composition Algebras and Their Automorphisms....Pages 310-327
Nilpotent Elements in Semi-simple Jordan Algebras....Pages 329-340
A Note on Three Dimensional Simple Lie Algebras....Pages 341-366
Some Groups of Transformations defined by Jordan Algebras. I....Pages 367-378
Some groups of Transformations defined by Jordan Algebras. III....Pages 379-387
MacDonald’s Theorem on Jordan algebras....Pages 388-405
A Coordinatization Theorem for Jordan Algebras....Pages 406-430
A Note on Automorphisms of Lie Algebras....Pages 431-455
Generic Norm of an Algebra....Pages 457-466
Clifford Algebras for Algebras with Involution of Type D....Pages 468-474
Corrections....Pages 475-487
Back Matter....Pages 489-514
....Pages 516-528