  We introduce a multi-parameter twisted Hopf algebra associated with a root
datum and show that its modified form is isomorphic to Lusztig's modified
quantum algebra under certain restrictions on the parameters. By taking various
specializations of the parameters, we obtain similar results for
two/multi-parameter quantum algebras and Kang-Kashiwara-Oh's multi-parameter
quantum superalgebras. As a consequence, the categories of weight modules of
these algebras are identical.
