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Abstract / Description of output
Let $\Bbbk$ be a field of characteristic zero. For any positive integer $n$ and any scalar $a\in\Bbbk$, we construct a family of Artin-Schelter regular algebras $R(n,a)$, which are quantisations of Poisson structures on $\Bbbk[x_0,\dots,x_n]$. This generalises an example given by Pym when $n=3$. For a particular choice of the parameter $a$ we obtain new examples of Calabi-Yau algebras when $n\geq 4$. We also study the ring theoretic properties of the algebras $R(n,a)$. We show that the point modules of $R(n,a)$ are parameterised by a bouquet of rational normal curves in $\mathbb{P}^{n}$, and that the prime spectrum of $R(n,a)$ is homeomorphic to the Poisson spectrum of its semiclassical limit. Moreover, we explicitly describe ${\rm Spec}\ R(n,a)$ as a union of commutative strata.
Original language | English |
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Pages (from-to) | 32-86 |
Number of pages | 34 |
Journal | Nagoya mathematical journal |
Volume | 233 |
Early online date | 25 Sept 2017 |
DOIs | |
Publication status | Published - Mar 2019 |
Keywords / Materials (for Non-textual outputs)
- math.RA
- math.AG
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Dive into the research topics of 'A new family of Poisson algebras and their deformations'. Together they form a unique fingerprint.Projects
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Sue Sierra
- School of Mathematics - Personal Chair of Noncommutative Algebra
Person: Academic: Research Active