Quadratic relations of the deformed W-superalgebra Wq,t(sl(2|1))

@article{Kojima2019QuadraticRO,
  title={Quadratic relations of the deformed W-superalgebra Wq,t(sl(2|1))},
  author={Takeo Kojima},
  journal={arXiv: Quantum Algebra},
  year={2019}
}
  • T. Kojima
  • Published 5 December 2019
  • Mathematics
  • arXiv: Quantum Algebra
This paper is a continuation of study by J.Ding and B.Feigin. We find a bosonization of the deformed $W$-superalgebras ${\cal W}_{q t}(\mathfrak{sl}(2|1))$ that commutes up-to total difference with deformed screening currents. Using our bosonization, we derive a set of quadratic relations of generators of the deformed $W$-superalgebra ${\cal W}_{q t}(\mathfrak{sl}(2|1))$. The deformed $W$-superalgebra is independent of the choice of a Dynkin-diagram for the superalgebra $\mathfrak{sl}(2|1… 
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5 Citations

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References

SHOWING 1-10 OF 49 REFERENCES
COMMENTS ON THE DEFORMED WN ALGEBRA
We obtain an explicit expression for the defining relation of the deformed WN algebra, ${\rm DWA}(\widehat{\mathfrak{sl}}_N)_{q,t}$. Using this expression we can show that, in the q→1 limit, ${\rm…
Quantum toroidal algebra associated with $\mathfrak{gl}_{m|n}$
We introduce and study the quantum toroidal algebra $\mathcal{E}_{m|n}(q_1,q_2,q_3)$ associated with the superalgebra $\mathfrak{gl}_{m|n}$ with $m\neq n$, where the parameters satisfy $q_1q_2q_3=1$.…
Sugawara and Vertex Operator Constructions for Deformed Virasoro Algebras
Abstract.From the defining exchange relations of the $$\mathcal{A}_{{q,p}} {\left( {\widehat{{gl}}_{N} } \right)}$$ elliptic quantum algebra, we construct subalgebras which can be characterized as…
Quantum-algebras and elliptic algebras
AbstractWe define a quantum-algebra associated to $$\mathfrak{s}\mathfrak{l}_N $$ as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes…
The Elliptic Algebra U_{q,p}(sl_N^) and the Deformation of W_N Algebra
After reviewing the recent results on the Drinfeld realization of the face type elliptic quantum group B_{q,lambda}(sl_N^) by the elliptic algebra U_{q,p}(sl_N^), we investigate a fusion of the…
Quantized W-algebra of sl(2,1) : a construction from the quantization of screening operators
Starting from bosonization, we study the operator that commute or commute up-to a total difference with of any quantized screen operator of a free field. We show that if there exists a operator in…
The Integrals of Motion for the Deformed W-Algebra Wqt(sl_N^)
We review the deformed W -algebra Wq,t(ŝlN ) and its screening currents. We explicitly construct the Local Integrals of Motion In (n = 1, 2, · · ·) for this deformed W -algebra. We explicitly…
On the defining relations of the affine Lie superalgebras and their quantized universal enveloping superalgebras
In this paper, we give defining relations of the affine Lie superalgebras an and defining relations of a super-version of the Drinfeld[D]-Jimbo[J] affine quantized universal enveloping algebras. As a…
Drinfeld–Sokolov Reduction for Difference Operators and Deformations of -Algebras¶I. The Case of Virasoro Algebra
Abstract:We propose a q-difference version of the Drinfeld-Sokolov reduction scheme, which gives us q-deformations of the classical -algebras by reduction from Poisson-Lie loop groups. We consider in…
On ω-Lie superalgebras
Let [Formula: see text] be a finite-dimensional vector space over a field [Formula: see text] of characteristic zero, [Formula: see text] an anti-commutative product on [Formula: see text] and…
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