Refinement of Ado's Theorem in Low Dimensions and Application in Affine Geometr
| Autor: | Yi-Fang Kang, Chengming Bai |
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| Rok vydání: | 2007 |
| Předmět: |
Pure mathematics
Algebra and Number Theory 17B 53C Zero (complex analysis) FOS: Physical sciences Mathematical Physics (math-ph) Base (topology) Ado's theorem Affine geometry Faithful representation Affine representation Mathematics - Quantum Algebra Lie algebra FOS: Mathematics Quantum Algebra (math.QA) Affine transformation Mathematical Physics Mathematics |
| DOI: | 10.48550/arxiv.0711.3836 |
| Popis: | 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. Comment: 11 pages, 4 tables, appear in Communications in Algebra |
| Databáze: | OpenAIRE |
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