Gröbner-Shirshov bases for Lie superalgebras and their universal enveloping algebras

DOI10.1006/jabr.1998.7810zbMath0931.17008arXivmath/9809024OpenAlexW2075463528WikidataQ115395825 ScholiaQ115395825MaRDI QIDQ1305008

Kyu-Hwan Lee, Peter Malcolmson, Seok-Jin Kang, Leonid A. Bokut'

Publication date: 27 February 2000

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9809024

zbMATH Keywords

Gröbner-Shirshov basesKac-Moody superalgebrasdefining relations of Lie superalgebrasuniversal enveloping algebras of Lie superalgebras

Mathematics Subject Classification ID

Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Universal enveloping (super)algebras (17B35) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Identities, free Lie (super)algebras (17B01) Universal enveloping algebras of Lie algebras (16S30)

Related Items (21)

Representations of spin quiver Hecke algebras for orthosymplectic Lie superalgebras ⋮ Linear algebraic approach to Gröbner-Shirshov basis theory ⋮ GR BNER–SHIRSHOV BASES FOR THE KAC–MOODY ALGEBRAS OF THE TYPE ⋮ Unnamed Item ⋮ Gröbner–Shirshov bases theory for Leibniz superalgebras ⋮ Gröbner–Shirshov bases method for Gelfand–Dorfman–Novikov algebras ⋮ Gröbner–Shirshov basis method for multiple tensor products of some associative algebras ⋮ Composition-diamond lemma for associative conformal algebras. ⋮ Gröbner-Shirshov bases for Vinberg-Koszul-Gerstenhaber right-symmetric algebras ⋮ Unnamed Item ⋮ Gröbner–Shirshov bases of the Lie algebra $D^{+}_{n}$ ⋮ Gröbner–Shirshov bases and their calculation ⋮ GRÖBNER-SHIRSHOV BASES FOR COXETER GROUPS ⋮ MONOMIAL BASES FOR SOME IRREDUCIBLE 𝔤₂-MODULES ⋮ Composition-diamond lemma for modules ⋮ HNN-extension of Lie superalgebras ⋮ Gröbner-Shirshov bases for associative algebras with multiple operators and free Rota-Baxter algebras. ⋮ Gröbner-Shirshov Bases for Exceptional Lie Superalgebras ⋮ Koszul algebras and Donaldson-Thomas invariants ⋮ Gröbner-Shirshov bases for irreducible \(sl_{n+1}\)-modules ⋮ Embedding into 2-generated simple associative (Lie) algebras

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