Some remarks on Koszul algebras and quantum groups
Manin, Yu. I.
Annales de l'Institut Fourier, Tome 37 (1987), p. 191-205 / Harvested from Numdam
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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},
     volume = {37},
     year = {1987},
     pages = {191-205},
     doi = {10.5802/aif.1117},
     mrnumber = {89e:16022},
     zbl = {0625.58040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1987__37_4_191_0}
}

Manin, Yu. I. Some remarks on Koszul algebras and quantum groups. Annales de l'Institut Fourier, Tome 37 (1987) pp. 191-205. doi : 10.5802/aif.1117. http://gdmltest.u-ga.fr/item/AIF_1987__37_4_191_0/

[1] V. G. Drinfeld, Quantum groups, Zap. Naučn. sem. LOMI, vol. 155 (1986), 18-49 (in russian). | MR 88f:17017 | Zbl 0617.16004

[2] S. B. Priddy, Koszul resolutions, Trans. AMS, 152-1 (1970), 39-60. | MR 42 #346 | Zbl 0261.18016

[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 88f:16030 | Zbl 0595.16020

[4] V. V. Lyubashenko, Hopf algebras and vector-symmetries, Uspekhi Mat. Nauk, 41-5 (1986), 185-186 (in russian). | MR 88c:58007 | Zbl 0649.16008

[5] P. Deligne, J. Milne, Tannakian categories, Springer lecture Notes in Math., vol. 900 (1982), 101-228. | MR 84m:14046 | Zbl 0477.14004

[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 89c:58048 | Zbl 0783.58025