Simple associative $\Gamma$-conformal algebras of finite type for a torsion-free group $\Gamma$

We study $\Gamma$-conformal algebras which are a discrete analog of conformal algebras in the sense of V. G. Kac. For a torsion-free group $\Gamma$, simple and semisimple associative $\Gamma$-conformal algebras of finite type are described and an analog of Wedderburn's theorem is proved.