Narrow Results

We present an $L_{\infty }$-algebra description of the Freedman–Townsend tensor gauge theory with an emphasis on the Maurer–Cartan homotopy action form using cyclic inner product. It is explicitly shown that the gauge variations, the conservation law and the dynamics of the theory are all incorporated in the underlying $L_{\infty }$-products. Also, following the more convenient method for reducible gauge theory, we propose the Batalin–Vilkovisky formalism of Freedman–Townsend model within the framework of $L_{\infty }$-algebras.