Standard Envelopes of Commutative Triple Systems

Abstract

Under certain constraints on the characteristic of a field Φ, the commutative standard enveloping q-algebra >B of a commutative triple system A over Φ is defined. It is proved that

(1) if the algebra B is simple, then the system A is simple;

(2) if the system A is simple, then B either is simple or decomposes into the direct sum of two isomorphic simple subalgebras (as of ideals).