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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 6, Pages 1228–1264 (Mi izv1339)  

This article is cited in 1 scientific paper (total in 1 paper)

Simple Lie algebras in varieties generated by Lie algebras of cartan type

Yu. P. Razmyslov


Abstract: The author proves that if $K$ is the algebra of regular functions of any smooth affine indecomposable algebraic variety ($\operatorname{char}K=0$) then it can be recovered from its Lie algebra of regular vector fields using a certain multilinear polynomial mapping. It is established that if, for some natural number $n$, a finitely generated Lie algebra $\mathscr G$ over an algebraically closed field $K$ ($\operatorname{char}K=0$) satisfies all identities of the Lie algebra $\widetilde W_n(K)$ of all derivations of the power series algebra in $n$ commuting variables, then $\mathscr G$ contains a proper subalgebra of finite codimension; moreover, for any maximal ideal $J$ of $\mathscr G$, either $\dim_K\mathscr G/J\leqslant n^2+2n$ or $\mathscr G/J$ can be embedded in $\widetilde W_n(K)$.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1988, 31:3, 541–573

Bibliographic databases:

UDC: 519.4
MSC: Primary 17B20; Secondary 17B65
Received: 10.04.1986

Citation: Yu. P. Razmyslov, “Simple Lie algebras in varieties generated by Lie algebras of cartan type”, Izv. Akad. Nauk SSSR Ser. Mat., 51:6 (1987), 1228–1264; Math. USSR-Izv., 31:3 (1988), 541–573

Citation in format AMSBIB
\Bibitem{Raz87}
\by Yu.~P.~Razmyslov
\paper Simple Lie~algebras in varieties generated by Lie algebras of cartan type
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 6
\pages 1228--1264
\mathnet{http://mi.mathnet.ru/izv1339}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=933963}
\zmath{https://zbmath.org/?q=an:0677.17018|0646.17012}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 31
\issue 3
\pages 541--573
\crossref{https://doi.org/10.1070/IM1988v031n03ABEH001089}


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    This publication is cited in the following articles:
    1. M. V. Zaicev, D. Repovš, “Exponential growth of codimensions of identities of algebras with unity”, Sb. Math., 206:10 (2015), 1440–1462  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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