Yangian double

Khoroshkin, S.; Tolstoy, V. N.

doi:10.1007/bf00714404

Cited by 99 publications

(152 citation statements)

References 8 publications

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“…Even though there are standard methods how to construct the Yangian including its universal R-matrix for simple Lie algebras [25], there are several reasons why we cannot apply them in a simple fashion for our system. The main one seems to be the peculiar situation that our algebra psu(2|2) R 3 has a non-trivial centre.…”

Section: Introduction and Overviewmentioning

confidence: 99%

The Classical r-Matrix of AdS/CFT and its Lie Bialgebra Structure

Beisert

Spill

2008

Commun. Math. Phys.

137

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Section: Introduction and Overviewmentioning

confidence: 99%

The Classical r-Matrix of AdS/CFT and its Lie Bialgebra Structure

Beisert

Spill

2008

Commun. Math. Phys.

137

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“…As a further check, we have computed the scalar factor as it comes from evaluating the universal R-matrix [36,37] on the all-level Yangian representation (2.5), and found that, after unitarization, it precisely coincides with (4.26). More precisely, the universal R-matrix reads 27) where R E and R F are certain factors depending on the Yangian generators associated to the positive and negative roots of the algebra, and…”

Section: Crossing Symmetry and S Matrixmentioning

confidence: 99%

Multi-parametric R-matrix for the $\mathfrak {sl}(2|1)$sl(2|1) Yangian

Babichenko

Торриелли

2012

Journal of Mathematical Physics

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We study the Yangian of the sl(2|1) Lie superalgebra in a multi-parametric fourdimensional representation. We use Drinfeld's second realization to independently rederive the R-matrix, and to obtain the antiparticle representation, the crossing and the unitarity condition. We consistently apply the Yangian antipode and its inverse to the individual particles involved in the scattering. We explicitly find a scalar factor solving the crossing and unitarity conditions, and study the analytic structure of the resulting dressed R-matrix. The formulas we obtain bear some similarities with those familiar from the study of integrable structures in the AdS/CFT correspondence, although they present obvious crucial differences.

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“…In [23] the universal R-matrix for the Yangian double of sℓ 2 has been found in a form of a product of three power series in generators S, S ± , Eq. (2).…”

Section: Introductionmentioning

confidence: 99%

Matrix Factorization for Solutions of the Yang–Baxter Equation

Derkachov

Chicherin

2016

J Math Sci

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We study solutions of the Yang-Baxter equation on a tensor product of an arbitrary finitedimensional and an arbitrary infinite-dimensional representations of the rank one symmetry algebra. We consider the cases of the Lie algebra sℓ 2 , the modular double (trigonometric deformation) and the Sklyanin algebra (elliptic deformation). The solutions are matrices with operator entries. The matrix elements are differential operators in the case of sℓ 2 , finite-difference operators with trigonometric coefficients in the case of the modular double, or finite-difference operators with coefficients constructed out of Jacobi theta functions in the case of the Sklyanin algebra. We find a new factorized form of the rational, trigonometric, and elliptic solutions, which drastically simplifies them. We show that they are products of several simply organized matrices and obtain for them explicit formulae.

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Yangian double

Cited by 99 publications

References 8 publications

The Classical r-Matrix of AdS/CFT and its Lie Bialgebra Structure

The Classical r-Matrix of AdS/CFT and its Lie Bialgebra Structure

Multi-parametric R-matrix for the $\mathfrak {sl}(2|1)$sl(2|1) Yangian

Matrix Factorization for Solutions of the Yang–Baxter Equation

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