Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2016.08.24
  • Accepted : 2016.12.26
  • Published : 2017.09.01
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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

Acknowledgement

Supported by : National Natural Science Foundation of China

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