Gröbner-Shirshov bases and PBW theorems

Abstract

We review some applications of Gröbner-Shirshov bases, including PBW theorems, linear bases of free universal algebras, normal forms for groups and semigroups, extensions of groups and algebras, embedding of algebras.

13 pages

References in corpus (5)

• Gröbner-Shirshov bases for Lie algebras over a commutative algebra
• Groebner-Shirshov bases for Schreier extensions of groups
• Groebner-Shirshov Basis for the Chinese Monoid
• Composition-Diamond lemma for associative $n$-conformal algebras
• Gröbner-Shirshov Bases for Commutative Algebras with Multiple Operators and Free Commutative Rota-Baxter Algebras