Hodge, Terrell L.; Parshall, Brian J. On the representation theory of Lie triple systems. (English) Zbl 1012.17001 Trans. Am. Math. Soc. 354, No. 11, 4359-4391 (2002). New results concerning the representation theory and cohomology theory of Lie triple systems are presented in this article. For a Lie triple system \(T\), let \(L_u (T) = \mathfrak L/\mathfrak I\) where \(\mathfrak L\) is the free Lie algebra based on \(T\), and \(\mathfrak I\) is the ideal in \(\mathfrak L\) generated by the elements \([a,b,c]-[[a,b],c]\) for \(a,b,c \in T\). Assume that the characteristic of the base field is not 2, and let \(\theta : L_u (T) \rightarrow L_u (T)\) be the involution with \(-1\) -eigenspace \(T\). The authors consider the precise relationship of the category of \(T\)-modules to the category of modules of \(L_u (T)\) that have a compatible action of \(\theta\). 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