✍ Scribed by Huishi Li (auth.)
No coin nor oath required. For personal study only.
This self-contained monograph is the first to feature the intersection of the structure theory of noncommutative associative algebras and the algorithmic aspect of Groebner basis theory. A double filtered-graded transfer of data in using noncommutative Groebner bases leads to effective exploitation of the solutions to several structural-computational problems, e.g., an algorithmic recognition of quadric solvable polynomial algebras, computation of GK-dimension and multiplicity for modules, and elimination of variables in noncommutative setting. All topics included deal with algebras of (q-)differential operators as well as some other operator algebras, enveloping algebras of Lie algebras, typical quantum algebras, and many of their deformations.
Algorithms
📜 SIMILAR VOLUMES
In this paper, we study conditions on algebras with multiplicative bases so that there is a Gröbner basis theory. We introduce right Gröbner bases for a class of modules. We give an elimination theory and intersection theory for right submodules of projective modules in path algebras. Solutions to h
We show how the complexity of counting relates to the well known phenomenon that computing Gröbner bases under a lexicographic order is generally harder than total degree orders. We give simple examples of polynomials for which it is very easy to compute their Gröbner basis using a total degree orde