From Semigroups to Groups

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


In this chapter, we show that for quantum semigroups like \(E={{\mathrm{\underline{end}}}}(A)\) or \({{\mathrm{\underline{e}}}}(A, g)\) there exists a universal map \(\gamma :E\rightarrow H\) into a Hopf algebra \(H\). In view of Proposition  3.7, \(\gamma \) makes all multiplicative matrices in \(E\) invertible. Hence a natural idea is to add, formally, the necessary inverse matrices. The following construction suffices to treat \({{\mathrm{\underline{end}}}}(A)\) and \({{\mathrm{\underline{e}}}}(A, g)\).

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Max Planck Institute for MathematicsBonnGermany

Personalised recommendations