Quantum groups under very strong axioms

Teo Banica¹

¹ Department of Mathematics University of Cergy-Pontoise F-95000 Cergy-Pontoise, France

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 67 (2019) no. 1, pp. 83-99.

Résumé

We study the intermediate quantum groups $H_N\subset G\subset U_N^+$. The basic examples are $H_N,K_N,O_N,U_N,H_N^+,K_N^+,O_N^+,U_N^+$, which form a cube. Any other example $G$ sits inside the cube, and by using standard operations, namely intersection $\cap $ and generation $\langle\,,\rangle $, can be projected on the faces and edges. We prove that under the strongest possible axioms, namely (1) easiness, (2) uniformity, and (3) geometric coherence of the various projection operations, the eight basic solutions are the only ones.

Détail

DOI : 10.4064/ba190128-8-3

Keywords: study intermediate quantum groups subset subset basic examples n n which form cube other example sits inside cube using standard operations namely intersection cap generation nbsp langle rangle projected faces edges prove under strongest possible axioms namely nbsp easiness nbsp uniformity nbsp geometric coherence various projection operations eight basic solutions only