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Examples of Peirce decomposition of generalized Jordan triple systems of second order. II: Balanced classical cases. (English) Zbl 1120.17003

Balanced GJTS of second order are a class of triple systems from which \({\mathbb Z}\)-graded Lie algebras of the form \(L=L_{-2} \oplus L_{-1} \oplus L_0 \oplus L_1 \oplus L_2\) can be constructed, where the vector spaces \(L_{-2}\) and \(L_2\) have dimension \(\leq 1\) [J. R. Faulkner, Trans. Am. Math. Soc. 155, 397–408 (1971; Zbl 0215.38503), N. Kamiya, General algebra, Proc. Conf., Vienna/Austria 1990, Contrib. Gen. Algebra 7, 205–213 (1991; Zbl 0743.17005)]. In the paper under review the author provides explicit forms of these triple systems and their Peirce decompositions in the classical cases.

MSC:

17A40 Ternary compositions
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
17C27 Idempotents, Peirce decompositions
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