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

Madras); R. Chakrabarti (Univ. Madras); R. Jagannathan (IMS

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

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arxiv hep-th/9409161 v1 pith:KGCIMYPF submitted 1994-09-27 hep-th math.QA

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 (Univ. Madras) , R. Jagannathan (IMS , Madras) This is my paper

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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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