# Filtrations and Distortion in Infinite-Dimensional Algebras - Mathematics > Rings and Algebras

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Abstract: A tame filtration of an algebra is defined by the growth of its terms, whichhas to be majorated by an exponential function. A particular case is the degreefiltration used in the definition of the growth of finitely generated algebras.The notion of tame filtration is useful in the study of possible distortion ofdegrees of elements when one algebra is embedded as a subalgebra in another. Ageometric analogue is the distortion of the Riemannian metric of a Liesubgroup when compared to the metric induced from the ambient Lie group. Thedistortion of a subalgebra in an algebra also reflects the degree of complexityof 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 orLie algebras, if a tame filtration of an algebra can be induced from the degreefiltration of a larger algebra.

Author: ** Yuri Bahturin, Alexander Olshanskii**

Source: https://arxiv.org/