Infinite-Dimensional代数中的滤子与畸变
Filtrations and Distortion in Infinite-Dimensional Algebras
摘要：
代数的驯服滤子由其项的增长来定义，其增长必须由指数函数来优化。一个特殊的情况是度过滤用于定义的增长的生成代数。在研究一个代数作为子代数嵌入到另一个代数中时，元素的度的可能变形时，驯服过滤的概念是有用的。一个几何类比是（李群）的（黎曼）度量与周围（李群）的度量相比的失真。一个代数中的子代数的畸变也反映了这个代数的元素在这个子代数中的隶属问题的复杂程度。我们在这里的目标之一是调查，主要是在结合或李代数的情况下，如果一个代数的驯服过滤可以从一个更大的代数的度过滤。
英文摘要：
A tame filtration of an algebra is defined by the growth of its terms, which has to be majorated by an exponential function. A particular case is the degree filtration used in the definition of the growth of finitely generated algebras. The notion of tame filtration is useful in the study of possible distortion of degrees of elements when one algebra is embedded as a subalgebra in another. A geometric analogue is the distortion of the (Riemannian) metric of a (Lie) subgroup when compared to the metric induced from the ambient (Lie) group. The distortion of a subalgebra in an algebra also reflects the degree of complexity of the membership problem for the elements of this algebra in this subalgebra. One of our goals here is to investigate, mostly in the case of associative or Lie algebras, if a tame filtration of an algebra can be induced from the degree filtration of a larger algebra.
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