论文标题
差分编码和指数增长
Differential codimensions and exponential growth
论文作者
论文摘要
让$ a $为有限的维数代数，在特征零的字段中具有派生，即，一个代数，其结构的结构被派生的lie代数$ l $的作用所丰富，而Let $ c_n^l（a），$ $ $ n \ n \ geq 1，$ n \ geq 1，$是其差异化的编码序列。这样的序列是指数界的，$ \ exp^l（a）= \ lim_ {n \ to \ infty} \ sqrt [n] {c_n^l（a）} $是一个可以计算的整数，称为$ a $ a $ a $的差异pi-expents。 在本文中，我们证明，对于任何lie代数$ l $，$ \ exp^l（a）$与$ \ exp（a）$，$ a $的普通pi exponent重合。此外，如果$ l $是可解决的谎言代数，我们将这种结果应用于几乎多项式增长的$ l $代数，即指数级增长的品种，以使任何适当的亚体变量都具有多种物质的增长。
Let $A$ be a finite dimensional associative algebra with derivations over a field of characteristic zero, i.e., an algebra whose structure is enriched by the action of a Lie algebra $L$ by derivations, and let $c_n^L(A),$ $n\geq 1,$ be its differential codimension sequence. Such sequence is exponentially bounded and $\exp^L(A) = \lim_{n\to \infty}\sqrt[n]{c_n^L(A)}$ is an integer that can be computed, called differential PI-exponent of $A$. In this paper we prove that for any Lie algebra $L$, $\exp^L(A)$ coincides with $\exp(A)$, the ordinary PI-exponent of $A$. Furthermore, in case $L$ is a solvable Lie algebra, we apply such result to classify varieties of $L$-algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety has polynomial growth.
