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Mat. Sb., 2019, Volume 210, Number 11, Pages 103–128 (Mi msb9132)  

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.

Funding Agency Grant Number
Russian Science Foundation 19-11-00172
This research was supported by the Russian Science Foundation under grant no. 19-11-00172.


DOI: https://doi.org/10.4213/sm9132

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English version:
Sbornik: Mathematics, 2019, 210:11, 1609–1632

Bibliographic databases:

UDC: 512.554.35
MSC: 14R20
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

Citation in format AMSBIB
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