ON 2-GENERATING INDEX OF FINITE DIMENSIONAL LEFT-SYMMETRIC ALGEBRAS
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In this paper, we introduce the notion of generating index $\I_1(A)$ ($2$-generating index $\I_2(A)$, resp.) of a left-symmetric algebra $A$, which is the maximum of the dimensions of the subalgebras generated by any element (any two elements, resp.). We give a classification of left-symmetric algebras with $\I_1(A)=1$ and $\I_2(A)=2,3$ resp., and show that all such algebras can be constructed by linear and bilinear functions. Such algebras can be regarded as a generalization of those relating to the integrable (generalized) Burgers equation.
Abstract
In this paper, we introduce the notion of generating index $\I_1(A)$ ($2$-generating index $\I_2(A)$, resp.) of a left-symmetric algebra $A$, which is the maximum of the dimensions of the subalgebras generated by any element (any two elements, resp.). We give a classification of left-symmetric algebras with $\I_1(A)=1$ and $\I_2(A)=2,3$ resp., and show that all such algebras can be constructed by linear and bilinear functions. Such algebras can be regarded as a generalization of those relating to the integrable (generalized) Burgers equation.
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