Embedding tensors on Lie triple systems

Abstract

In this paper, first we introduce the notion of embedding tensors on Lie triple systems and show that embedding tensors induce naturally 3-Leibniz algebras. Next, we construct a Lie
3-algebra whose Maurer-Cartan elements are embedding tensors. Then, we have the twisted
$L_{\infty}$-algebra that governs deformations of embedding tensors. Following this, we establish the cohomology of an embedding
tensor on a Lie triple system and realize it as the cohomology of the induced 3-Leibniz algebra with coefficients in a suitable
representation. As applications, we consider infinitesimal and finite order deformations of an embedding tensor on a Lie triple system from
a cohomological viewpoint.