Interacting D2-branes in 10 dimensions and non abelian Born-Infeld theory

In this paper we extend the bosonic $D$-brane action in D=10 obtained by duality from the D=11 membrane wrapped on $S^1$ to an SU(2) non abelian system. This system presents only first class constraints, whose algebra closes off-shell and generalizes the algebra of diffeomorphisms of the $D2$-brane to include non abelian symmetry generators. From the SU(2) $D$-brane action, we also obtain the SU(2) Born-Infeld theory by performing a covariant reduction to a flat background. This calculation agrees up to fourth order with the result obtained from the superstring amplitudes and gives an alternative approach to analyze non-abelian Born-Infeld theories.