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2:30-3:20: ľꇵ֘׼Մ

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3:30-4:20: Drinfeld double of deformed quantum algebras

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4:30-5:20: ʾһЩơ

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Title: Drinfeld double of deformed quantum algebras
Abstract: 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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}ĿSome new trends in representation algebra

ժҪRepresentation algebra or representation ring provides a natural framework

for the study of tensor category (such as the category of _nite dimensional repre-

sentations over group algebra, Lie algebra, Hopf algebra and quantum groups),

and has been proven useful in representation theory and other _elds. In this

talk, we will recall a little bit history and basic properties of representation ring

and representation algebra, and then report some new trends in representation

algebras of some classes of Hopf algebras and applications.

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