Mathematics – Quantum Algebra
Scientific paper
2001-07-19
Mathematics
Quantum Algebra
18 pages, ams-latex
Scientific paper
Let $\bar{Pr}$ denote the ideal spanned by the characters of projective modules in the Grothendieck ring of the category of finite dimensional modules over the small quantum group $u_l$. We show that $\bar{Pr}$ admits a description completely parallel to that of the Verlinde algebra of the fusion category, restricted over $u_l$, with the character of the Steinberg module playing the role of the identity.
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