Titlebook: Nathan Jacobson Collected Mathematical Papers; Volume 2 (1947–1965) Nathan Jacobson Book 1989 Birkhäuser Boston 1989 algebra.automorphism.c

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Derivation Algebras and Multiplication Algebras of Semi-Simple Jordan Algebrasith a finite basis) over a field of characteristic 0. We show that the derivation algebra . possesses a certain ideal . consisting of derivations that we call inner and that . is also a subalgebra of the Lie multiplication algebra .. For semi-simple algebras we prove that . This result is a conseque

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Enveloping Algebras of Semi-Simple Lie Algebrasn quantum mechanics. In our paper we gave a method of determining the matrix solutions of such equations. The starting point of our discussion was the observation that if the elements .. satisfy (1) then the elements .., [.., ..] satisfy the multiplication table of a certain basis of the Lie algebra

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Some Remarks on One-Sided Inverses, where it is understood that .. = l =... It can be verified directly that the .. thus defined satisfy the multiplication table for matrix units:.In particular the elements .. = .. are orthogonal idempotent elements. No ..=0. For by (3) the vanishing of one of the .. implies the vanishing of all; in

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Operator Commutativity in Jordan algebras.→. = . of .. The notion of .-commutativity has been introduced by Jordan, Wigner, and von Neumann [.] who called this concept simply commutativity. Since every Jordan algebra is commutative in the usual sense, the above change in terminology seems to be desirable. In this note we shall study the no

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Structure of Alternative and Jordan Bimodulesciative algebras or in the class of Lie algebras, then this notion is the familiar one for which we are in possession of well-worked theories. The study of bimodules (or representations) of Jordan algebras was initiated by the author in a recent paper [21]. Subsequently the alternative case was cons