Abstract
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 \({{\mathrm{\underline{e}}}}(A, g)\).
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Notes
- 1.
Hereafter \(\mathbb {K}\langle Z_0, Z_1,\cdots \rangle \) and similar expressions denote the algebra freely generated by the matrix entries.
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Manin, Y.I. (2018). From Semigroups to Groups . In: Quantum Groups and Noncommutative Geometry. CRM Short Courses. Springer, Cham. https://doi.org/10.1007/978-3-319-97987-8_8
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DOI: https://doi.org/10.1007/978-3-319-97987-8_8
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