摘要: Let Ω be an arbitrary family of non-isomorphic n-dimensional alternative algebras over algebraically closed field k that depends continuously on a certain set of parameters p_1,...,p_N. Then the asymptotic of the dimension of Ω, t... 展开 Let Ω be an arbitrary family of non-isomorphic n-dimensional alternative algebras over algebraically closed field k that depends continuously on a certain set of parameters p_1,...,p_N. Then the asymptotic of the dimension of Ω, that is the largest possible number N of parameters, is4/27n~3+ O(n~(8/3)). We also formulate a conjecture for the asymptotic of the 7 number of parameters to define irreducible family of n-dimensional Jordan algebras, namely N =1/6 (3)~(1/2) +0(n~(8/3)). We prove it for some closed subvariety of the variety of Jordan algebras. 收起