考察辛代数的Peirce分解.在此过程中应用了Meyberg K.关于结合代数的Peirce分解,利用结合代数的幂等元,得到了辛代数的Peirce分解,并得出2个重要定理.
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.
[1] FAULKNER J R, FERRAR J C. On the structure of symplectic ternary algebras [J]. Indagationes Mathematicae 1972, 34.
[2] 刘绍学. 环与代数 [M]. 北京:科学出版社 1983.
[3] FARRAR J C. Strictly regular elements in Freudenthal triple systems [J]. Transactions of the American Mathematical Society 1972, 174.
[4] MEYBERG K. Lectures on algebras and triple systems [M]. Chrlottesville:Virginia University Press 1972.
