7
$\begingroup$

Let $\frak{g}$ be a simple Lie algebra of A,B,C,or D series type. Moreover, let $U_q(\frak{g})$ be its Drinfeld-Jimbo quantized enveloping algebra, and $G_q$ the quantized enveloping algebra. As is shown, for example, in Chapter 9 of Klimyk and Schmudgen, each $G_q$ can be realized as a quotient of an FRT algebra (which is to say, roughly, that they can be constructed from an R-matrix in the Yang--Baxter sense).

Does such a presentation exist for the exceptional quantum groups $E_q(6)$, $E_q(7), E_q(8), F_q(4)$, and $G_q(2)$?

$\endgroup$
1
$\begingroup$

I think a good reference is this paper by Jin-Ma. R-matrices for E7 and F4 are computed while references are given for E6 and G2. I am not aware if E8 has been taken care of.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.