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Classification of Quantum Groups via Galois Cohomology
Journal article, 2020

The aim of the present paper is to extend these results to all twisted Belavin–Drinfeld cohomology and thus, to present classification of quantum groups in terms of Galois cohomology and the so-called orders. Low dimensional cases sl(2) and sl(3) are considered in more details using a theory of cubic rings developed by B. N. Delone and D. K. Faddeev in Delone and Faddeev (The theory of irrationalities of the third degree. Translations of mathematical monographs, vol 10. AMS, Providence, 1964). Our results show that there exist yet unknown quantum groups for Lie algebras of the types An, D2n+1, E6, not mentioned in Etingof et al. (J Am Math Soc 13:595–609, 2000).

## Author

### Eugene Karolinsky

V.N. Karazin Kharkiv National University

### Arturo Pianzola

Centro de Altos Estudios en Ciencia Exactas

University of Alberta

### Alexander Stolin

Chalmers, Mathematical Sciences, Algebra and geometry

#### Communications in Mathematical Physics

0010-3616 (ISSN) 1432-0916 (eISSN)

Vol. 377 2 1099-1129### Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

### DOI

10.1007/s00220-019-03597-z