Enriquez, Benjamin [Andruskiewitsch, N.] Integrity, integral closedness and finiteness over their centers of the coordinate algebras of quantum groups at \(p^ \nu\)-th roots of unity. (English) Zbl 0838.17012 Ann. Sci. Math. Qué. 19, No. 1, 21-47 (1995). The author proves that coordinate algebras dual to Lusztig’s quantum enveloping algebras at \(p^\nu\)-th roots of 1 are integral domains where \(p\) is a prime number not dividing the coefficients of the Cartan matrix. From this he deduces the same result if the parameter is transcendental. He also proves after a suitable \(p\)-adic completion that these coordinate algebras are finite over their centers and integrally closed in the sense of De Concini, Kac, and Procesi.In an appendix, written jointly with N. Andruskiewitsch, a Frobenius morphism is constructed in the non-simply connected case. The paper may be regarded as a contribution to the geometric theory of quantum group duals. Reviewer: W.M.McGovern (Seattle) Cited in 3 Documents MSC: 17B37 Quantum groups (quantized enveloping algebras) and related deformations 16W30 Hopf algebras (associative rings and algebras) (MSC2000) Keywords:integrity; integral closedness; root of unity; coordinate algebras; Frobenius morphism; quantum group PDFBibTeX XMLCite \textit{B. Enriquez}, Ann. Sci. Math. Qué. 19, No. 1, 21--47 (1995; Zbl 0838.17012)