The Peirce decomposition for generalized Jordan triple systems of finite order

Every tripotent e of a generalized Jordan triple system J of order l uniquely defines a decomposition into the direct sum of l2+2l components. This decomposition generalizes the known Peirce decomposition of a Jordan triple system and of a generalized Jordan triple system of second order, and is the first step in determining the structure of a generalized Jordan triple system in terms of the tripotent.