Gröbner-Shirshov bases and their calculation
arXiv:1303.5366 · doi:10.1007/s13373-014-0054-6
Abstract
In this survey, we formulate the Gröbner-Shirshov bases theory for associative algebras and Lie algebras. Some new Composition-Diamond lemmas and applications are mentioned.
91 pages
References in corpus (8)
- Differential Type Operators and Gröbner-Shirshov Bases
- Structure of Leavitt path algebras of polynomial growth
- Gröbner-Shirshov bases for Lie algebras over a commutative algebra
- Gröbner-Shirshov bases for semirings
- Lyndon-Shirshov basis and anti-commutative algebras
- Triangular decomposition of right coideal subalgebras
- Groebner-Shirshov bases for Schreier extensions of groups
- Groebner-Shirshov basis for HNN extensions of groups and for the alternating group
Cited by in corpus (25)
- Gelfand--Dorfman algebras, derived identities, and the Manin product of operads
- Gröbner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras
- On the special identities of Gelfand--Dorfman algebras
- Groebner-Shirshov bases for pre-associative algebras
- Noncommutative Novikov algebras
- Construction of free differential algebras by extending Gröbner-Shirshov bases
- Free objects and Gröbner-Shirshov bases in operated contexts
- HNN-extension of Lie superalgebras
- Free Rota-Baxter systems and a Hopf algebra structure
- Algebras defined by Lyndon words and Artin-Schelter regularity
- A new Composition-Diamond lemma for dialgebras
- Standard bases for the universal associative conformal envelopes of Kac--Moody conformal algebras
- Universal enveloping algebra of a pair of compatible Lie brackets
- A new Composition-Diamond lemma for associative conformal algebras
- Tangent complexes and the Diamond Lemma
- On formulas and some combinatorial properties of Schubert Polynomials
- Universal enveloping commutative Rota-Baxter algebras of precommutative and postcommutative algebras
- Context-free languages and associative algebras with algebraic Hilbert series
- On the pre-commutative envelopes of commutative algebras
- Free operated monoids and Rewriting systems
- Derivations of Leavitt path algebra
- Parafree augmented algebras and Gröbner-Shirshov bases for complete augmented algebras
- Koszulity, supersolvability, and Stirling representations
- Hochschild cohomology of the Weyl conformal algebra with coefficients in finite modules
- Automaticity of one-relator semigroups with length less than or equal to three