Abstract
We examine families of twists by an automorphism of the complex polynomial ring on n generators. The multiplication in the twisted algebra determines a Poisson structure on affine n-space. We demonstrate that if the automorphism has a single eigenvalue, then the primitive ideals in the twist are parameterized by the algebraic symplectic leaves associated to this Poisson structure. Furthermore, in this case all of the leaves are algebraic and can be realized as the orbits of an algebraic group.
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Brandl, M.K. Primitive and Poisson Spectra of Single-Eigenvalue Twists of Polynomial Algebras. Algebr Represent Theor 9, 241–258 (2006). https://doi.org/10.1007/s10468-006-9008-3
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DOI: https://doi.org/10.1007/s10468-006-9008-3