The twisted presentation conjecture for the quantum affine algebra of sl2\mathfrak{sl}_2

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Let Uq(sl2^)U_q(\widehat{\mathfrak{sl}_2}) denote the quantum affine algebra. Let the twisted algebra be generated by a1ma_{1m} for m∈2Z+1m\in 2\mathbb Z+1, by γ\gamma, and by x1n±x_{1n}^{\pm} for n∈Zn\in\mathbb Z, subject to the relations associated to A1A_1. Twisted presentation conjecture. The quantum affine algebra Uq(sl2^)U_q(\widehat{\mathfrak{sl}_2}) is isomorphic to this twisted algebra. The statement identifies the standard quantum affine algebra with the algebra defined by the displayed twisted current relations, giving an alternative presentation in type A1A_1.

References

Primary source

Naihuan Jing, “New twisted quantum current algebras”, arXiv:math/9901066 (1999).

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