%0 Journal Article %T On the quantum superalgebra U_q(gl(m,n)) and its representations at roots of 1 %A Chaowen Zhang %J Mathematics %D 2012 %I arXiv %X An purely algebraic proof of the PBW theorem of U_q(gl(m,n)) is given. Lusztig's conjecture is extended to the super case. The Lusztig's tensor product theorem is established. %U http://arxiv.org/abs/1211.4115v4