  We develop a symmetric analog of brace algebras and discuss the relation of
such algebras to $L_{\infty}$-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 $L_{\infty}$-algebras that result from a
particular gauge theory for massless particles of high spin.
