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Jordan, David A.
Ore extensions and Poisson algebras. (English) Zbl 1372.16025
Glasg. Math. J. 56, No. 2, 355-368 (2014).
Summary: For a derivation \(\delta\) of a commutative Noetherian \(\mathbb C\)-algebra \(A\), a homeomorphism is established between the prime spectrum of the Ore extension \(A[z;\delta]\) and the Poisson prime spectrum of the polynomial algebra \(A[z]\) endowed with the Poisson bracket such that \(\{A,A\}=0\) and \(\{z,a\}=\delta(a)\) for all \(a \in A\).

Cited in 6 Documents
MSC:
16S36 Ordinary and skew polynomial rings and semigroup rings
13N15 Derivations and commutative rings
17B63 Poisson algebras
Keywords:
derivation of commutative Noetherian \(\mathbb C\)-algebra; homeomorphism; prime spectrum of Ore extension; Poisson prime spectrum of polynomial algebra
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\textit{D. A. Jordan}, Glasg. Math. J. 56, No. 2, 355--368 (2014; Zbl 1372.16025)
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