Vol. 15, No. 4, 1965

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On simple algebras obtained from homogeneous general Lie triple systems

Arthur Argyle Sagle

Vol. 15 (1965), No. 4, 1397–1400

We continue the investigation of the simple anti-commutative algebras obtained from a homogeneous general L.t.s. In particular we consider the algebra which satisfies

J(x,y,z)w = J (w, x,yz)+ J(w,y,zx)+ J(w,z,xy).

The usual process of analyzing a nonassociative algebra is to decompose it relative to elements whose right and left multiplications are diagonalizable linear transformations e.g. idempotents or Cartan subalgebras. In this paper we show that such a process yields only Lie algebras and indicates the difficulty in finding any non-Lie multiplication table for a simple anticommutative algebra satisfying (1).

Mathematical Subject Classification
Primary: 17.30
Received: 3 August 1964
Published: 1 December 1965
Arthur Argyle Sagle