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http://dx.doi.org/10.4134/JKMS.j160556

ON 2-GENERATING INDEX OF FINITE DIMENSIONAL LEFT-SYMMETRIC ALGEBRAS  

Yang, Xiaomei (LPMC and School of Mathematical Sciences Nankai University)
Zhu, Fuhai (LPMC and School of Mathematical Sciences Nankai University)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.5, 2017 , pp. 1537-1556 More about this Journal
Abstract
In this paper, we introduce the notion of generating index ${\mathcal{I}}_1(A)$ (2-generating index ${\mathcal{I}}_2(A)$, 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 ${\mathcal{I}}_1(A)=1$ and ${\mathcal{I}}_2(A)=2$, 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.
Keywords
left-symmetric algebra; generating index; non-associative algebra; linear function;
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