Résumé

In this talk, we will explain how the Kauffman bracket relations can be derived using the representation theory of Uq(sl2). We will introduce the stated skein algebra and show that the stated skein algebra of a bigon is Oq(SL2), while the stated skein algebra of the once-punctured monogon corresponds to the transmutation of Oq(SL2). Finally, we will introduce the Oq(SL2)-comodule structure of the stated skein algebra.

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