The Tannaka–Krein Formalism and (Re)Presentations of Universal Quantum Groups

  • Yuri I. Manin
Part of the CRM Short Courses book series (CRMSC)


In this chapter we expand upon Section  14.8 of the present volume, where the possibility of “hidden symmetry” in algebraic geometry was discussed. More precisely, our goal is to convince the reader that, as long as one starts with a reasonable algebra \(A\), the universal bi- and Hopf algebras \({{\mathrm{\underline{end}}}}(A)\) and \({{\mathrm{\underline{gl}}}}(A)\) introduced in Chapters  5 and  8 are well-behaved objects.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Max Planck Institute for MathematicsBonnGermany

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