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filtered ring

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Definition

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

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.


filtered objects

associated graded objects

References

Last revised on November 25, 2019 at 09:33:26. See the history of this page for a list of all contributions to it.