Refinement of Ado's Theorem in Low Dimensions and Application in Affine Geometr

Details Refinement of Ado's Theorem in Low Dimensions and Application in Affine Geometr Refinement of Ado's Theorem in Low Dimensions and Application in Affine Geometr

2007-11-24

arxiv.org/abs/0711.3836v1

Communications in Algebra 36 (2008) 82-93

Mathematics

Quantum Algebra

11 pages, 4 tables, appear in Communications in Algebra

Scientific paper

10.1080/00927870701649382

In this paper, we construct a faithful representation with the lowest dimension for every complex Lie algebra in dimension $\leq 4$. In particular, in our construction, in the case that the faithful representation has the same dimension of the Lie algebra, it can induce an \'etale affine representation with base zero which has a natural and simple form and gives a compatible left-symmetric algebra on the Lie algebra. Such affine representations do not contain any nontrivial one-parameter subgroups of translation.

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