Bialgebras and Hopf Algebras

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


Let H be a \(\mathbb {K}\)-module. Recall that a bialgebra structure on H is defined by four morphisms
$$\begin{aligned} H\otimes H&\xrightarrow {m} H \xrightarrow {\varDelta } H\otimes H\;,\\ \mathbb {K}&\xrightarrow {\eta } H \xrightarrow {\varepsilon } \mathbb {K}\;, \end{aligned}$$
satisfying the following axioms, written as commutative diagrams.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Max Planck Institute for MathematicsBonnGermany

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