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1
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A family of regular vertex operator algebras with two generators

100%
Adamović D.
Open Mathematics
|
2007
|
tom 5
|
nr 1
1-18
EN
For every m ∈ ℂ ∖ {0, −2} and every nonnegative integer k we define the vertex operator (super)algebra D m,k having two generators and rank $$\frac{{3m}}{{m + 2}}$$ . If m is a positive integer then D m,k can be realized as a subalgebra of a lattice vertex algebra. In this case, we prove that D m,k is a regular vertex operator (super) algebra and find the number of inequivalent irreducible modules.
2
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The 3-state Potts model and Rogers-Ramanujan series

81%
Feingold A., Milas A.
Open Mathematics
|
2013
|
tom 11
|
nr 1
1-16
EN
We explain the appearance of Rogers-Ramanujan series inside the tensor product of two basic A 2(2) -modules, previously discovered by the first author in [Feingold A.J., Some applications of vertex operators to Kac-Moody algebras, In: Vertex Operators in Mathematics and Physics, Berkeley, November 10–17, 1983, Math. Sci. Res. Inst. Publ., 3, Springer, New York, 1985, 185–206]. The key new ingredients are (5,6)Virasoro minimal models and twisted modules for the Zamolodchikov W 3-algebra.
3
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Embedding of dendriform algebras into Rota-Baxter algebras

81%
Gubarev V., Kolesnikov P.
Open Mathematics
|
2013
|
tom 11
|
nr 2
226-245
EN
Following a recent work [Bai C., Bellier O., Guo L., Ni X., Splitting of operations, Manin products, and Rota-Baxter operators, Int. Math. Res. Not. IMRN (in press), DOI: 10.1093/imrn/rnr266] we define what is a dendriform dior trialgebra corresponding to an arbitrary variety Var of binary algebras (associative, commutative, Poisson, etc.). We call such algebras di- or tri-Var-dendriform algebras, respectively. We prove in general that the operad governing the variety of di- or tri-Var-dendriform algebras is Koszul dual to the operad governing di- or trialgebras corresponding to Var!. We also prove that every di-Var-dendriform algebra can be embedded into a Rota-Baxter algebra of weight zero in the variety Var, and every tri-Var-dendriform algebra can be embedded into a Rota-Baxter algebra of nonzero weight in Var.
4
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Quasi-particle fermionic formulas for (k, 3)-admissible configurations

61%
Jerković M., Primc M.
Open Mathematics
|
2012
|
tom 10
|
nr 2
703-721
EN
We construct new monomial quasi-particle bases of Feigin-Stoyanovsky type subspaces for the affine Lie algebra sl(3;ℂ)∧ from which the known fermionic-type formulas for (k, 3)-admissible configurations follow naturally. In the proof we use vertex operator algebra relations for standard modules and coefficients of intertwining operators.
5
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Combinatorial bases of modules for affine Lie algebra B 2(1)

61%
Primc M.
Open Mathematics
|
2013
|
tom 11
|
nr 2
197-225
EN
We construct bases of standard (i.e. integrable highest weight) modules L(Λ) for affine Lie algebra of type B 2(1) consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces W(Λ) of L(Λ) by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence W(kΛ0) for B 2(1) and the integrable highest weight module L(kΛ0) for A 1(1) have the same parametrization of combinatorial bases and the same presentation P/I.
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