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filtered ring

Contents

Definition

A filtered ring (resp. filtered algebra) is a monoid object in the category of filtered abelian groups (resp. filtered vector space?s).

One considers positive and negative filtrations, as well as \mathbb{Z}-filtrations.

To-do list: complete filtrations, associated graded ring, symbol map, Poisson structure on the associated graded algebra if the latter is commutative.

Examples

A major example is the universal enveloping algebra of any Lie algebra.

See also Lazard's criterion and microlocalization.

References

Revised on October 18, 2012 21:46:04 by Zoran Škoda (161.53.130.104)