Abstract
We provide a deformation, fβ, of Lusztig algebra f. Various quantum algebras in literatures, including half parts of two-parameter quantum algebras, quantum superalgebras, and multi-parameter quantum algebras/superalgebras, are all specializations of fβ. Moreover, fβ is isomorphic to Lusztig algebra f up to a twist. As a consequence, half parts of those quantum algebras are isomorphic to Lusztig algebra f over a big enough ground field up to certain twists. We further construct the entire algebra Uβ,ξ by Drinfeld double construction. As special cases, above quantum algebras all admit a Drinfeld double construction under certain assumptions.
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