Some new aspects of supersymmetry<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi></mml:math>-parity violating interactions

We examine $R$-parity-breaking interactions with lepton-number violation in the minimal supergravity model and obtain new stringent bounds on the coupling constants from low-energy processes. We discuss the decay of the lightest supersymmetric particle and analyze possible signatures for $R$-parity-violating interactions in $W$, $Z$, and Higgs-boson decays, and in ${e}^{+}{e}^{\ensuremath{-}}$ collisions.