Simple left-symmetric algebras with¶solvable Lie algebra
Simple left-symmetric algebras with¶solvable Lie algebra
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DOI：
10.1007/s002290050037
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发表时间：
1998-03
影响因子：
0.6
通讯作者：
D. Burde
中科院分区：
文献类型：
--
作者：
D. Burde
左对称代数（LSA）是从几何学中产生的李容许代数。李群{G}上的左不变仿射结构与其李代数上的LSA-结构双射对应。此外，如果李群简单传递地充当向量空间上的仿射变换，则其李代数具有完整的LSA结构。在本文中，我们研究简单的LSA只有平凡的双边理想。一些自然的例子和变形。我们对低维的简单LSA进行了分类，并利用标准根空间分解证明了关于简单LSA的李代数的结果。研究了一类特殊的完备LSA。
Left-symmetric algebras (LSAs) are Lie admissible algebras arising from geometry. The leftinvariant affine structures on a Lie group {G} correspond bijectively to LSA-structures on its Lie algebra. Moreover if a Lie group acts simply transitively as affine transformations on a vector space, then its Lie algebra admits a complete LSA-structure. In this paper we studysimpleLSAs having only trivial two-sided ideals. Some natural examples and deformations are presented. We classify simple LSAs in low dimensions and prove results about the Lie algebra of simple LSAs using a canonical root space decomposition. A special class of complete LSAs is studied.