Geodesic
An~estimate of the number of parameters defining an~$n$-dimensional algebra
Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 283-294.

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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. 
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Yu. A. Neretin. An~estimate of the number of parameters defining an~$n$-dimensional algebra. Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 283-294. http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a4/

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