Noncommutative Gröbner Bases and Ext Groups

Abstract

We consider a theory of noncommutative Gröbner bases on decreasingly filtered algebras whose associated graded algebras are commutative. We transfer many algorithms that use commutative Gröbner bases to this context. As a result, we have a very efficient way to compute Ext groups for a large class of graded algebras. This has many applications especially in algebraic topology.

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Keywords

Noncommutative Gröbner Bases / Steenrod algebra / Adams spectral sequence / Homological algebra / 13P10 / 14F35 / 55S10

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Funding

China Postdoctoral Science Foundation(2021TQ0015)

Fundamental Research Funds for the Central Universities

RIGHTS & PERMISSIONS

Peking University