论文标题
Nilpotent二次谎言代数的等效结构
Equivalent constructions of nilpotent quadratic Lie algebras
论文作者
论文摘要
双扩展和t*扩展是用于构建有限维二次谎言代数的经典方法。第一个给出了特征性零的感应性分类，而最新的分类产生了二次非缔合代数（不仅是谎言），其特征与2的特征不同。二骨nilpotent Lie代数的分类也可以减少到宽松的nilpotent lie Algebras及其无algebras及其无名主义形式的研究中。在这项工作中，我们将在这三种构造方法中建立同等表征。这种等效性将二次2步nilpotent的分类降低了自然方式与三位杆菌的分类。此外，理论结果将为他们之间的切换提供简单的规则。
The double extension and the T*-extension are classical methods for constructing finite dimensional quadratic Lie algebras. The first one gives an inductive classification in characteristic zero, while the latest produces quadratic non-associative algebras (not only Lie) out of arbitrary ones in characteristic different from 2. The classification of quadratic nilpotent Lie algebras can also be reduced to the study of free nilpotent Lie algebras and their invariant forms. In this work we will establish an equivalent characterization among these three construction methods. This equivalence reduces the classification of quadratic 2-step nilpotent to that of trivectors in a natural way. In addition, theoretical results will provide simple rules for switching among them.
