Equivariant one-parameter deformations of Lie triple systems
Lie triple systems were first noted by E. Cartan in his studies on totally geodesic submanifolds of Lie groups and on symmetric spaces. Lie triple systems were studied from the algebraic point of view by \textit{N. Jacobson} [Trans. Am. Math. Soc. 70, 509--530 (1951; Zbl 0044.02503)] and \textit{W. G. Lister} [Trans. Am. Math. Soc. 72, 217--242 (1952; Zbl 0046.03404)]. The deformation is a tool to study a mathematical object by deforming it into a family of the same kind of objects depending on a certain parameter. Algebraic deformation theory was introduced by \textit{M. Gerstenhaber} [Ann. Math. (2) 84, 1--19 (1966; Zbl 0147.28903)] for rings and algebras. The deformation theory for Lie triple systems is introduced by \textit{F. Kubo} and \textit{Y. Taniguchi} [J. Algebra 278, No. 1, 242--250 (2004; Zbl 1065.17010)]. In this article, the authors introduced equivariant formal deformation theory of Lie triple systems. They introduced an equivariant deformation cohomology of Lie triple systems and using this they studied the equivariant formal deformation theory of Lie triple systems.
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