We provide a deformation, $f_{\alpha, \beta}$, of Lusztig algebra $f$. Various quantum algebras in literature, including half parts of two-parameter quantum algebras, quantum superalgebras, and multi-parameter quantum algebras/superalgebras, are all specializations of $f_{\alpha, \beta}$. Moreover, $f_{\alpha, \beta}$ 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 $U_{\beta, \xi}$ by Drinfeld double construction. As special cases, above quantum algebras all admit a Drinfeld double construction under certain assumptions. This is a joint work with Junjing Xing.
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樊赵兵，哈尔滨工程大学理学院教授、博导，国际交流与合作处处长，黑龙江省杰出青年基金获得者。2012年毕业于美国堪萨斯州立大学，获博士学位；2012-2015年先后于美国纽约州立大学布法罗分校、美国堪萨斯州立大学从事博士后和访问助理教授工作。主要从事几何表示论及其相关领域的研究，在Mem. Amer. Math. Soc.、Trans. Amer. Math. Soc.、Comm. Math. Phys.、Int Math. Res. Not.、J. Algebra等国际高水平期刊上发表学术论文近二十篇，主持国家自然科学基金面上项目一项。
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