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The electroweak unification group $ SU(2)_L\times SU(2)_R\times SU(2)_Y $ isproposed for the charged lepton flavor violating decays of the muon ($\mu$) andtau ($\tau$) leptons. The group $SU(2)_Y$ is in the lepton space. Theleft-handed leptons and anti-leptons are assigned to the fundamentalrepresentation $(2,2,\bar{2})$ of the semi-simple group. The gauge group$SU(2)_Y$ is spontaneously broken to $U(1)_{Y_1}$, where $Y_1=-L=\pm1$ is thehypercharge, by introducing a scalar multiplet $\Sigma$ which belongs to thetriplet representation 3 of the $SU(2)_Y$ and is singlet under $SU(2)_L\timesSU(2)_R$. At this stage charged vector bosons $Y^\pm$ of $SU(2)_Y$ whichmediate the lepton flavor violating decays acquire masses and are decoupledwith one Higgs scalar $H_\Sigma^0$. The residual group $SU(2)_L\timesSU(2)_R\times U(1)_{Y_1}$ has all the features of the left-right electroweakunification group extensively studied in the literature. The probability forlepton flavor violating decays is$\left(\frac{\sin^2\theta_W}{1-2\sin^2\theta_W}\right)^2\left(\frac{m_{W_L}}{m_Y}\right)^4$.

Lepton flavour violating decays of $\mu$ and $\tau$ lepton in a gauge group $SU_L(2)\times SU_R(2)\times SU_l(2)$