The space of periodic Boehmians with $Delta$-convergence is a complete topological algebra which is not locally convex. A family of Boehmians ${T_lambda}$ such that $T_0$ is the identity and $T_{lambda_1+lambda_2}=T_lambda_1*T_lambda_2$ for all real numbers $lambda_1$ and $lambda_2$ is called a one-parameter group of Boehmians. We show that if ${T_lambda}$ is strongly continuous at zero, then ${T_lambda}$ has an exponential representation. We also obtain some results concerning the infinitesimal generator for ${T_lambda}$.