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

An identification of Lusztig's modified forms of quantum algebras and their analogues