Automorphisms of quantum and classical Poisson algebras

Details Automorphisms of quantum and classical Poisson algebras Automorphisms of quantum and classical Poisson algebras

2002-11-11

arxiv.org/abs/math/0211175v1

Compositio Math. 140 (2004), 511-527.

Mathematics

Rings and Algebras

LaTeX, 20 pages

Scientific paper

We prove Pursell-Shanks type results for the Lie algebra D(M) of all linear differential operators of a smooth manifold M, for its Lie subalgebra D^1(M) of all linear first-order differential operators of M, and for the Poisson algebra S(M)=Pol(T*M) of all polynomial functions on the cotangent bundle T*M, the symbols of the operators in D(M). Chiefly however we provide explicit formulas describing completely the automorphisms of the Lie algebras D^1(M), S(M), and D(M).

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