Uq(sl(m+1))-Module Algebra Structures on the Coordinate Algebra of a Quantum Vector Space

In this paper, the module-algebra structures of U q (sl(m + 1)) = H(e i , f i , k 1 i ) 1im on the coordinate algebra of quantum vector spaces are studied.We denote the coordinate algebra of quantum n -dimensional vector space by A q (n) .As our main result, first, we give a complete classification of module-algebra structures of U q (sl(m + 1)) on A q (3) when k i Aut L(A q (3)) as actions on A q (3) for i = 1, , m and m 2 and with the same method, on A q (2) , all module-algebra structures of U q (sl(m + 1)) are characterized.Lastly, the module-algebra structures of U q (sl(m + 1)) on A q (n) are obtained for any n 4 .