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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
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
Citation:
Yu. A. Neretin, “An estimate of the number of parameters defining an $n$-dimensional algebra”, Math. USSR-Izv., 30:2 (1988), 283–294
Linking options:
https://www.mathnet.ru/eng/im1295https://doi.org/10.1070/IM1988v030n02ABEH001010 https://www.mathnet.ru/eng/im/v51/i2/p306
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Abstract page: | 461 | Russian version PDF: | 160 | English version PDF: | 11 | References: | 75 | First page: | 3 |
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