关键词: 辛代数, Peirce分解, 幂等元, 严格正交

Abstract: The main purpose of this note is to study a Peirce decomposition for a symplectic algebra.The authors define the symplectic algebra by identities which are modified from the symplectic algebra in the paper on the structure of symplectic ternary algebras of Faulkner J R and Ferrar J C.but it is more comprehensive.Throughout the authors assume symplectic algebras over algebraically closed fields of characteristic zero unless otherwise specified.