Algebra theory MOC Poisson algebra A Poisson algebra (π΄, β ,[ β , β ]) is an K-monoid (π΄, β ) and Lie algebra (π΄,[ β , β ]) such that the Lie bracket (called the Poisson bracket) is a derivation, falg i.e. [π₯,π¦π§]=[π₯,π¦]π§+π¦[π₯,π§] whence follows [π₯π¦,π§]=[π₯,π§]π¦+π₯[π¦,π§] Examples Any K-monoid with its Commutator forms a Poisson algebra tidy | en | SemBr