Poisson brackets and two-generated subalgebras of rings of polynomials

By I. Shestakov, Ualbai U. Umirbaev. 2003

120 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/36a9543b092a79cb997e7a0366b8c2c5b375c97f

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In Geometry and Topology

1. Ualbai U. Umirbaev

In Mathematical Physics

1. Ualbai U. Umirbaev

Citations in the corpus

• Universal enveloping algebras and universal derivations of Poisson algebras (2011, background): “p ∂xi hxn, ∂p ∂xi ∈ Pe, for all 1 ≤ i≤ n. For every endomorphism ψof the free Poisson algebra Pwe define the Jacobian matrix J(ψ) = [uij] with uij = ∂ψ(x i) ∂x j for all 1 ≤ i,j≤ n. It is easy to show [27] that J(ψ) is invertible over Peif ψis an automorphism. The reverse statement is an analogue of ”