Maximally extended \({\mathfrak{sl}}(2|2)\) as a quantum double (Q2834792)

This paper is concerned with the question of identifying a universal R-matrix (that is, a solution to the Yang-Baxter equation) giving rise to the R-matrices for two important integrable models, namely the Hubbard model and AdS/CFT.NEWLINENEWLINEThere is a well-known method to try to construct such universal R-matrices, by constructing the quantum double of a Hopf algebra. The double is always quasi-triangular and thus has an associated R-matrix. From previous work of the first author and collaborators (beginning with [\textit{N. Beisert} and \textit{P. Koroteev}, J. Phys. A, Math. Theor. 41, No. 25, Article ID 255204, 47 p. (2008; Zbl 1163.81009)]), what is needed to solve the problem is (a quotient of) a quantum double that contains a particular quantized enveloping algebra, namely \(U_{q}(\mathfrak{psl}(2|2) \ltimes \mathbb{C}^{3})\). The required algebra is identified here as having the form \(U_{q,\kappa}(\mathfrak{sl}(2)\ltimes \mathfrak{psl}(2|2) \ltimes \mathbb{C}^{3})\), wherein three additional boost operators have been introduced, along with an additional parameter \(\kappa\). A presentation is given for this algebra as well as an explicit description of its universal R-matrix.