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On the Hopf structure of $U_{p,q}(gl(1|1))$ and the universal ${\cal T}$-matrix of $Fun_{p,q}(GL(1|1))$

R. Chakrabarti·R. Jagannathan
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Abstract

Using the technique developed by Fronsdal and Galindo (Lett. Math. Phys. 27 (1993) 57) for studying the Hopf duality between the quantum algebras $Fun_{p,q}(GL(2))$ and $U_{p,q}(gl(2))$, the Hopf structure of $U_{p,q}(gl(1|1))$, dual to $Fun_{p,q}(GL(1|1))$, is derived and the corresponding universal ${\cal T}$-matrix of $Fun_{p,q}(GL(1|1))$, embodying the suitably modified exponential relationship $U_{p,q}(gl(1|1))$ $\rightarrow$ $Fun_{p,q}(GL(1|1))$, is obtained.

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R. Chakrabarti, R. Jagannathan. 1994-09-27. On the Hopf structure of $U_{p,q}(gl(1|1))$ and the universal ${\cal T}$-matrix of $Fun_{p,q}(GL(1|1))$. https://arxiv.org/abs/hep-th/9409161

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