A Dixmier-moeglin Equivalence for Skew Laurent Polynomial Rings
نویسنده
چکیده
The work of Dixmier in 1977 and Moeglin in 1980 show us that for a prime ideal P in the universal enveloping algebra of a complex finite-dimensional Lie algebra the properties of being primitive, rational and locally closed in the Zariski topology are all equivalent. This equivalence is referred to as the Dixmier-Moeglin equivalence. In this thesis we will study skew Laurent polynomial rings of the form C[x1, . . . , xd][z, z−1; σ] where σ is a C-algebra automorphism of C[x1, . . . , xd]. In the case that σ restricts to a linear automorphism of the vector space C + Cx1 + · · · + Cxd, we show that the Dixmier-Moeglin equivalence holds for the prime ideal (0).
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