Vol. 83, No. 2, 1979

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Peirce ideals in Jordan triple systems

Kevin Mor McCrimmon

Vol. 83 (1979), No. 2, 415–439
Abstract

We show that an ideal in a Peirce space Ji (i = 1,12,0) of a Jordan triple system J is the Peirce i-component of a global ideal precisely when it is invariant under the multiplications L(J12,J12), P(J12)P(J12) (for i = 1); under L(J12,J12), P(J12)P(J12), P(J12)P(e)P(J12), L(J12,e)P(J0,J12) (for i = 0); under L(J1), L(J0), L(J12,e)L(e,J12), L(J12,e)P(e,J12) (for i = 12). 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
Authors
Kevin Mor McCrimmon