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This article is cited in 1 scientific paper (total in 1 paper)
Commuting homogeneous locally nilpotent derivations
D. A. Matveev Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia
Abstract:
Let $X$ be an affine algebraic variety endowed with an action of complexity one of an algebraic torus $\mathbb T$. It is well known that homogeneous locally nilpotent derivations on the algebra of regular functions $\mathbb K[X]$ can be described in terms of proper polyhedral divisors corresponding to the $\mathbb T$-variety $X$. We prove that homogeneous locally nilpotent derivations commute if and only if a certain combinatorial criterion holds. These results are used to describe actions of unipotent groups of dimension two on affine $\mathbb T$-varieties.
Bibliography: 10 titles.
Keywords:
$\mathbb T$-variety, graded algebra, locally nilpotent derivation, additive group action.
Received: 12.05.2018 and 10.02.2019
Citation:
D. A. Matveev, “Commuting homogeneous locally nilpotent derivations”, Mat. Sb., 210:11 (2019), 103–128; Sb. Math., 210:11 (2019), 1609–1632
Linking options:
https://www.mathnet.ru/eng/sm9132https://doi.org/10.1070/SM9132 https://www.mathnet.ru/eng/sm/v210/i11/p103
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Abstract page: | 293 | Russian version PDF: | 32 | English version PDF: | 3 | References: | 30 | First page: | 14 |
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