# New Supersymmetry Algebra

We know that SUSY generators commute with translation $$[P_\mu,Q_\alpha]=0$$ I have some questions:

1. What is this equation physical meaning?

2. Is it possible to make "SUSY-like" generators that do not commute with translation? $[P_\mu,Q_\alpha]\ne0$

3. What are the consequences of such relation?