Zhao, Lina; Li, Xuewen; Zhang, Zhixue Non-degenerate invariant bilinear forms on nonassociative triple systems. (English) Zbl 1067.17002 Chin. Ann. Math., Ser. B 26, No. 2, 275-290 (2005). A bilinear form \(f\) on a triple system \(\mathcal T\) over a field \(\mathcal F\) is said to be invariant if and only if \(f(\langle abc\rangle; d) = f(a; \langle dcb\rangle = f(c; \langle bad\rangle)\) for all \(a, b, c, d \in \mathcal T\). The authors investigate the uniqueness of decompositions of a finite-dimensional triple system \(\mathcal T\) as a direct sum of indecomposable ideals. For a triple system \(\mathcal T\) admitting a nondegenerate invariant bilinear form \(f\) they similarly investigate the decomposition of \(\mathcal T\) as the direct sum of \(f\)-indecomposable ideals; i.e. ideals that do not contain proper nonzero ideals \(\mathcal I\) with \(\mathcal I \cap \mathcal I^\perp = 0\). The final section contains applications to Lie triple systems. Reviewer: Gordon Brown (Boulder) Cited in 1 ReviewCited in 4 Documents MSC: 17A40 Ternary compositions 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.) PDFBibTeX XMLCite \textit{L. Zhao} et al., Chin. Ann. Math., Ser. B 26, No. 2, 275--290 (2005; Zbl 1067.17002) Full Text: DOI References: [6] doi:10.1007/978-1-4612-6398-2 · doi:10.1007/978-1-4612-6398-2 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.