Hopf \(*\)-Algebras and Compact Matrix Pseudogroups

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


Let \((H, m,\varDelta )\) be a Hopf \(\mathbb {C}\)-algebra with a bijective antipode \(i\). Drinfeld suggested to define a \(*\)-structure on \(H\) by means of an antilinear map \(j:E\rightarrow E\) with the following properties:
  1. (a)

    \(j\) is an isomorphism of algebras and an anti-isomorphism of coalgebras;

  2. (b)

    \(j^2= (ij)^2=\mathrm {id}\).


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Max Planck Institute for MathematicsBonnGermany

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