Peirce ideals in Jordan triple systems

Kevin Mor McCrimmon

Vol. 83 (1979), No. 2, 415–439

DOI: 10.2140/pjm.1979.83.415

Abstract

We show that an ideal in a Peirce space J_i (i = 1,1∕2,0) of a Jordan triple system J is the Peirce i-component of a global ideal precisely when it is invariant under the multiplications L(J_1∕2,J_1∕2), P(J_1∕2)P(J_1∕2) (for i = 1); under L(J_1∕2,J_1∕2), P(J_1∕2)P(J_1∕2), P(J_1∕2)P(e)P(J_1∕2), L(J_1∕2,e)P(J₀,J_1∕2) (for i = 0); under L(J₁), L(J₀), L(J_1∕2,e)L(e,J_1∕2), L(J_1∕2,e)P(e,J_1∕2) (for i = 1∕2). We use this to show that the sub triple systems J₁ and J₀ are simple when J is. The method of proof closely follows that for Jordan algebras, but requires a detailed development of Peirce relations in Jordan triple systems.

Mathematical Subject Classification 2000

Primary: 17C99

Milestones

Received: 20 October 1977

Published: 1 August 1979