论文标题
长度缓慢的代数
Algebras of slowly growing length
论文作者
论文摘要
我们研究了长度缓慢的有限维度的有限维度的缔合代数，也就是说，对于此类中的任何代数，其长度小于或等于其维度。我们表明，该类别非常大，特别是有限的维度代数以及许多其他重要的经典有限维数代数属于该类别，例如，莱布尼兹代数，诺维科夫代数和辛比尔代数。证明了这些代数长度的确切上限。为此，我们将特征序列的方法转移到非阴性代数，并在代数元素上找到某些多项式条件，以保证长度函数的缓慢生长。
We investigate the class of finite dimensional not necessary associative algebras that have slowly growing length, that is, for any algebra in this class its length is less than or equal to its dimension. We show that this class is considerably big, in particular, finite dimensional Lie algebras as well as many other important classical finite dimensional algebras belong to this class, for example, Leibniz algebras, Novikov algebras, and Zinbiel algebras. An exact upper bounds for the length of these algebras is proved. To do this we transfer the method of characteristic sequences to non-unital algebras and find certain polynomial conditions on the algebra elements that guarantee the slow growth of the length function.
