RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

 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

Full text: PDF file (764 kB)
First page: PDF file
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 512.554.35
MSC: 14R20

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
\Bibitem{Mat19} \by D.~A.~Matveev \paper Commuting homogeneous locally nilpotent derivations \jour Mat. Sb. \yr 2019 \vol 210 \issue 11 \pages 103--128 \mathnet{http://mi.mathnet.ru/msb9132} \crossref{https://doi.org/10.4213/sm9132} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2019SbMat.210.1609M} \elib{http://elibrary.ru/item.asp?id=43288573} \transl \jour Sb. Math. \yr 2019 \vol 210 \issue 11 \pages 1609--1632 \crossref{https://doi.org/10.1070/SM9132} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000508557700001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85082454214}