Poisson structure on sl(2)over a field of arbitrary characteristic
All Poisson structure on sl(2)is determined over a field of arbitrary characteristic by use of the definition and bilinear property of Poisson algebras.On one hand,over a field of characteristic not equal to 2,all Poisson structure on sl(2)depends on a variety,and none of them is associative or commutative except 0;On the other hand,over a field of characteristic 2,all Poisson structure on sl(2)depends on 8 varieties,and either associative or commutative or non-associative and non-commutative Poisson structure exists.
万方数据
维普
