Semisimple nil algebras of type δ

Tim Anderson and Erwin Kleinfeld

Vol. 76 (1978), No. 1, 9–16

DOI: 10.2140/pjm.1978.76.9

Abstract

We prove that a finite dimensional semisimple nil algebra over a field F which satisfies the identity (1 + δ)z(x ∘ y) + (1 − δ)(x ∘ y)z = x(y ∘ z) + y(x ∘ z), where δ ∈ F and δ≠ − 1∕2, is anti-commutative. This result permits a further reduction in the problem of classifying those varieties of power-associative algebras over F having the property that squares of ideals are ideals and for which the nil algebras are not pathological.

Mathematical Subject Classification 2000

Primary: 17D10

Milestones

Received: 23 February 1976

Revised: 9 August 1977

Published: 1 May 1978