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Any quasi-triangular Hopf algebra has an (in its completion) an element u called the Drinfeld element which gives an isomorphism from a representation to its double dual.

However, most people prefer to use a different pivotal structure on the category of representations of the quantized universal enveloping algebra, where u is replaced by g=v^-1u. Several obvious references don't seem to have a formula for this element, even though my dim recollection is that it is very simple. Is there anywhere where this is written down properly?

Any quantized universal enveloping algebra (in fact, any toplogically quasi-triangular Hopf algebra) has an (in its completion) an element u called the Drinfeld element which gives an isomorphism from a representation to its double dual.

However, most people prefer to use a different pivotal structure on the category of representations of the quantized universal enveloping algebra, where u is replaced by g=v^-1u. Several obvious references don't seem to have a formula for this element, even though my dim recollection is that it is very simple. Is there anywhere where this is written down properly?