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(i)(+/- 1))(1 <= i <= m)., 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-p(sl(m + 1)) on A(q)(3) when k(i) is an element of 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.