Quantum Divided Power Algebra And Its Duality

In this paper, based on the discussions on the quantum divided power algebra and the quantum restricted divided power algebra Aq in [1], we study the Uq(sln)-module structure of Aqv which is the dual module of Aq, and the Uq(sln)-module structure of Aq(?)Aqv. We also get the actions on Aq(?)Aqv by eij, fij, and discuss the decompositions of Aq(?)Aqv by studying the decompositions of the homogeneous space of Aq(?)Aqv while q is not a root of unity and the decompositions of (Aq(?)Aqv)a,0 while q is a root of unity and n=3.