Shirshov composition techniques in Lie superalgebras (noncommutative Gröbner bases)

DOI10.1007/BF02362521zbMath0862.17005MaRDI QIDQ1126540

Alexander A. Mikhalev

Publication date: 10 December 1996

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

zbMATH Keywords

Gröbner basisLyndon-Shirshov wordscolor Lie superalgebras

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Graded Lie (super)algebras (17B70) Computational methods for problems pertaining to nonassociative rings and algebras (17-08)

Related Items (13)

Primitive and almost primitive elements of Schreier varieties ⋮ Gröbner-Shirshov bases for semirings. ⋮ Generalized anti-commutative Gröbner-Shirshov basis theory and free Sabinin algebras ⋮ Unnamed Item ⋮ Gröbner–Shirshov basis method for multiple tensor products of some associative algebras ⋮ Gröbner-Shirshov bases for Lie algebras over a commutative algebra ⋮ Gröbner-Shirshov bases for Vinberg-Koszul-Gerstenhaber right-symmetric algebras ⋮ Gröbner–Shirshov bases of the Lie algebra $D^{+}_{n}$ ⋮ Gröbner–Shirshov bases and their calculation ⋮ Gröbner-Shirshov bases for Rota-Baxter algebras. ⋮ Gröbner–Shirshov bases for brace algebras ⋮ Gröbner-Shirshov bases for associative algebras with multiple operators and free Rota-Baxter algebras. ⋮ Monomial algebras

Cites Work

• A composition lemma and the equality problem for color Lie superalgebras
• Computing a Gröbner basis of a polynomial ideal over a Euclidean domain
• The diamond lemma for ring theory
• Embeddings into simple associative algebras
• Gröbner-Shirshov bases for exceptional Lie algebras. I
• The subalgebras of free Lie \(p\)-algebras
• On theories with a combinatorial definition of 'equivalence'
• On the Homology of Associative Algebras
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