The $\bm{e^- e^-}$ mode of LC: opportunities to discover loop-level lepton flavor (number) violation

The $e^- e^-$ mode with lepton number $L=+2$ of the initial state is particularly suitable for studying lepton and flavor number violating reactions (LFV). In this brief report we give a summary of the study of two loop-level reactions which violate lepton and flavor numbers: we first consider seesaw type models with heavy Majorana neutrinos at the TeV scale and study the reactions $e^{-}e^{-} \to \ell^{-}\ell^{-}$, and then similar reactions $e^{-}e^{-} \to \ell^{-}e^{-}$ ($\ell=\mu,\tau$) in supersymmetric models where LFV is due to slepton mixing.