six-dimensional phase space by setting $$G_1 = \exp(p_2 + \alpha q_3), G_2 = \exp(p_3 + \beta q_1), G_3 =
\exp(p_1 + \gamma q_2).$$ The covariant BRST charge for this model is equal to $$\begin{aligned}
\Omega &=&\eta^1 \, G_1 + \eta^2 \, G_2 + \eta^3 \, G_3 + \\
\nonumber
& & 1/2 \,
  (\alpha \,\eta^{2}\,\eta^{1}\,{{\cal P}}_{2}\,G_{1}
  -\alpha \,\eta^{2}\,\eta^{1}\,{{\cal P}}_{1}\,G_{2}
  -\beta \,\eta^{3}\,\eta^{2}\,{{\cal P}}_{3}\,G_{2} \\ \nonumber
& &\mbox{~~~~~~}
  -\beta \,\eta^{3}\,\eta^{2}\,{{\cal P}}_{2}\,G_{3}
  +\gamma \,\eta^{3}\,\eta^{1}\,{{\cal P}}_{3}\,G_{1}
  +\gamma \,\eta^{3}\,\eta^{1}\,{{\cal P}}_{1}\,G_{3}) + \\ \nonumber
& & 1/12 \, (
  ( - \alpha \,\beta +2\,\alpha \,\gamma  -\beta \,\gamma )
     \,\eta^{3}\,\eta^{2}\,\eta^{1}\,{{\cal P}}_{3}\,{{\cal P}}_{2}\,G_{1} + \\
\nonumber & &\mbox{~~~~~~~~~}
  ( -2\,\alpha \,\beta +\alpha \,\gamma +\beta \,\gamma )
     \,\eta^{3}\,\eta^{2}\,\eta^{1}\,{{\cal P}}_{3}\,{{\cal P}}_{1}\,G_{2} +\\
\nonumber & &\mbox{~~~~~~~~~}
  ( -\alpha \,\beta -\alpha \,\gamma +2\,\beta \,\gamma )
     \,\eta^{3}\,\eta^{2}\,\eta^{1}\,{{\cal P}}_{2}\,{{\cal P}}_{1}\,G_{3}
)\end{aligned}$$ and is of rank 2 (the maximum possible rank) unless $\alpha = \beta =
\gamma$, or $\alpha = \beta = 0$, $\gamma \neq 0$, in which case it is of rank 1.

Examples
========

We now give the BRST charge (or the first terms of the BRST charge) for some particular Poisson algebras. The examples have been treated using REDUCE, using the treatment of summation over dummy indices developed in [@Dre:CanExp; @Dre:Imacs]. Details 