Some remarks on Koszul algebras and quantum groups
Annales de l'Institut Fourier, Tome 37 (1987) no. 4, pp. 191-205.

La catégorie des algèbres quadratiques est munie d’une structure tensorielle. Ceci permet de construire des algèbres de Hopf du type “(semi) groupes quantiques”.

The category of quadratic algebras is endowed with a tensor structure. This allows us to construct a class of Hopf algebras studied recently under the name of quantum (semi) groups.

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     author = {Manin, Yu. I.},
     title = {Some remarks on {Koszul} algebras and quantum groups},
     journal = {Annales de l'Institut Fourier},
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Manin, Yu. I. Some remarks on Koszul algebras and quantum groups. Annales de l'Institut Fourier, Tome 37 (1987) no. 4, pp. 191-205. doi : 10.5802/aif.1117. http://www.numdam.org/articles/10.5802/aif.1117/

[1] V. G. Drinfeld, Quantum groups, Zap. Naučn. sem. LOMI, vol. 155 (1986), 18-49 (in russian). | MR | Zbl

[2] S. B. Priddy, Koszul resolutions, Trans. AMS, 152-1 (1970), 39-60. | MR | Zbl

[3] C. Löfwall, On the subalgebra generated by one-dimensional elements in the Yoneda Ext-algebra, Springer Lecture Notes in Math., vol. 1183 (1986), 291-338. | MR | Zbl

[4] V. V. Lyubashenko, Hopf algebras and vector-symmetries, Uspekhi Mat. Nauk, 41-5 (1986), 185-186 (in russian). | MR | Zbl

[5] P. Deligne, J. Milne, Tannakian categories, Springer lecture Notes in Math., vol. 900 (1982), 101-228. | MR | Zbl

[6] A. A. Beilinson, V. Ginsburg, Mixed categories, Ext-duality and representations, 1986, preprint.

[7] V. G. Drinfeld, On quadratic commutation relations in the quasiclassic limit, in : Mat. Fizika i Funke. Analiz, Kiev, Naukova Dumka (1986), 25-33 (in russian). | MR | Zbl

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