Symmetric Brace Algebras

We develop a symmetric analog of brace algebras and discuss the relation of such algebras to $L_{\mathrm{\infty }}$-algebras. We give an alternate proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie algebras. As an application, symmetric braces are used to describe transfers of strongly homotopy structures. We then explain how these symmetric brace algebras may be used to examine the $L_{\mathrm{\infty }}$-algebras that result from a particular gauge theory for massless particles of high spin.