1. Filtrations and Distortion in Infinite-Dimensional Algebras
- Author
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Alexander Yu. Olshanskii and Yuri Bahturin
- Subjects
Pure mathematics ,Algebra and Number Theory ,010102 general mathematics ,Subalgebra ,020207 software engineering ,Universal enveloping algebra ,02 engineering and technology ,Mathematics - Rings and Algebras ,01 natural sciences ,16S15, 16S30, 16P90, 17B65 ,Lie conformal algebra ,Graded Lie algebra ,Algebra ,Filtered algebra ,Lie algebras ,Rings and Algebras (math.RA) ,0202 electrical engineering, electronic engineering, information engineering ,Algebra representation ,FOS: Mathematics ,Cellular algebra ,0101 mathematics ,Associative algebras ,Generalized Kac–Moody algebra ,Mathematics ,Algebras given by generators and defining relations - Abstract
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.
- Published
- 2010
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