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Mathematics of the USSR-Izvestiya, 1988, Volume 30, Issue 2, Pages 283–294
DOI: https://doi.org/10.1070/IM1988v030n02ABEH001010
(Mi im1295)
 

This article is cited in 14 scientific papers (total in 14 papers)

An estimate of the number of parameters defining an $n$-dimensional algebra

Yu. A. Neretin
References:
Abstract: Consider an arbitrary family of nonisomorphic $n$-dimensional complex Lie algebras (respectively, associative algebras, commutative algebras) that depends continuously on a certain set of parameters $t_1,\dots,t_N\in\mathbf C$. The asymptotics is obtained for the largest number $N$ of parameters possible when $n$ is fixed: $\frac 2{27}n^3+O(n^{8/3})$, $\frac 4{27}n^3+O(n^{8/3})$, $\frac 2{27}n^3+O(n^{8/3})$ respectively. A decomposition into irreducible components is also studied for the algebraic variety $\text{Lie}_n$ of all possible Lie algebra structures on the linear space $\mathbf C^n$.
Bibliography: 19 titles.
Received: 18.02.1985
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1987, Volume 51, Issue 2, Pages 306–318
Bibliographic databases:
UDC: 519.4
MSC: Primary 16A46, 17B05; Secondary 16A58
Language: English
Original paper language: Russian
Citation: Yu. A. Neretin, “An estimate of the number of parameters defining an $n$-dimensional algebra”, Izv. Akad. Nauk SSSR Ser. Mat., 51:2 (1987), 306–318; Math. USSR-Izv., 30:2 (1988), 283–294
Citation in format AMSBIB
\Bibitem{Ner87}
\by Yu.~A.~Neretin
\paper An~estimate of the number of parameters defining an~$n$-dimensional algebra
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 2
\pages 306--318
\mathnet{http://mi.mathnet.ru/im1295}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=896999}
\zmath{https://zbmath.org/?q=an:0641.17012|0624.17008}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 30
\issue 2
\pages 283--294
\crossref{https://doi.org/10.1070/IM1988v030n02ABEH001010}
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  • https://doi.org/10.1070/IM1988v030n02ABEH001010
  • https://www.mathnet.ru/eng/im/v51/i2/p306
  • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:457
    Russian version PDF:156
    English version PDF:10
    References:74
    First page:3
     
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