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Abstract: This paper is devoted to analize inside the infinitely many possible bases ofUqg, same that can be considered -more equal then others-. The element ofselection has been a privileged relation with the bialgebra. A new parameter z-has been found that determines the commutation relations, independent from thez=logq that defines Uqg. Both z and z- are necessary to fix the relationsbetween the basic set and its coproducts. Three cases are particularlyrelevant: the analytical set with z-=z, the Lie set with Lie-like commutationrelations for z-=0 and the canonical-crystal basis with z- infinity. Tosimplify the exposition, we discuss in details the easy generalizable case ofUqsu2.



Author: Enrico Celeghini

Source: https://arxiv.org/



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