Composition-Diamond lemma for associative $n$-conformal algebras
By Leonid A. Bokut, Yuqun Chen, Guanglian Zhang. 2004
61 citations recorded by the source corpus.
In this paper, we study the concept of associative $n$-conformal algebra over a field of characteristic 0 and establish Composition-Diamond lemma for a free associative $n$-conformal algebra. As an application, we construct Gr\"{o}bner-Shirshov bases for Lie $n$-conformal algebras presented by generators and defining relations.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/674ca9401d619e190e3b02b84b48d495928c594f
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Citations in the corpus
- 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,”
- Varieties of dialgebras and conformal algebras (2006, background): “NG OF A DIALGEBRA 5 Multiply (13) with (· (2) c), c∈ B: (D(a(1) b)− a⊢ b+a⊣ b) (2) c= −2(a(1) b) (1) c= −2a(1) (b(1) c). Hence, a(1) (b(1) c) ∈ I(this is so-called composition of right multiplication [BFK1]). Next, multiply (13) with (· (1) c): (D(a(1) b) −a⊢ b+a⊣ b) (1) c = −(a(1) b) (0) c− (a⊢ b) ”
- Associative conformal algebras with finite faithful representation (2004, background): “nformal algebra, Weyl algebra, finite representation. Partially supported by RFBR and SSc-2269.2003. 1 2 PAVELKOLESNIKOV algebras (Grobner–Shirshov bases, Composition-Diamond lemma) were considered in [5, 6, 7]. The class of conformal algebras coincides with the class of pseudoalgebras [1, 3] over th”