GROBNER-SHIRSHOV BASES FOR REPRESENTATION THEORY

By Seok-Jin Kang, Kyu-Hwan Lee. 2000

63 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/804d44dd2a461d70c11f2225a09426cd4967a31c

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Citations in the corpus

Gröbner–Shirshov Bases for Irreducible sln + 1-Modules (2000, methodology): “In [15], we developed Gröbner–Shirshov basis theory for representations of associative algebras by introducing the notion of the Gröbner–Shirshov pair.”
Gröbner–Shirshov bases and their calculation (2013, background): “3.1.3 Braid groups in the Birman–Ko–Lee generators Recall that the Birman–Ko–Lee generators σts of the braid group Bn are σts = (σt−1σt−2 . . . σs+1)σs(σ−1s+1 · · · σ−1t−2σ−1t−1) and we have the presentation Bn = gp〈σts, n ≥ t > s ≥ 1|σtsσrq = σrqσts, (t − r)(t − q)(s − r)(s − q) > 0, σtsσsr = σtrσt”
Grobner-Shirshov Bases for Associative Algebras with Multiple Operators and Free Rota-Baxter Algebras ∗† (2008, background): “In recent years there were quite a few results on Gröbner-Shirshov bases for associative algebras, semisimple Lie (super) algebras, irreducible modules, Kac–Moode algebras, Coxeter groups, braid groups, conformal algebras, free inverse semigroups, Lodays’ dialgebras, Leibniz algebras and so on, see,”
Composition-Diamond lemma for associative $n$-conformal algebras (2004, unknown): “Last years there were quite a few results on Gröbner–Shirshov bases for semi-simple Lie (super) algebras, irreducible modules, Kac–Moody algebras, Coxeter groups, braid groups, quantum groups, conformal algebras, free inverse semigroups, Kurosh’s Ω-algebras, Loday’s dialgebras, Leibniz algebras, Rot”