Poisson Structure for Restricted Lie Algebras

  title={Poisson Structure for Restricted Lie Algebras},
  author={Victor G. Kac and Andrey Radul},
The Poisson bracket is an important invariant of a deformation of a commutative associative algebra A (cf. [D]). Given a family of associative (but not necessarily commutative) algebras Ah, such that Ao = A, one defines a Poisson bracket of two elements a, b € A by taking a(h), b(h) € A h , such that a(0)= a, b(0) = b and letting $$\left\{ {a,b} \right\} = \mathop {\lim }\limits_{h \to 0} {{[a\left( h \right),b(h)]} \over h}.$$ (1) 
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