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.

Funding

China Postdoctoral Science Foundation(2021TQ0015); Fundamental Research Funds for the Central Universities