no. 4
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.

@article{AIF_1987__37_4_191_0,
     author = {Manin, Yu. I.},
     title = {Some remarks on {Koszul} algebras and quantum groups},
     journal = {Annales de l'Institut Fourier},
     pages = {191--205},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {37},
     number = {4},
     year = {1987},
     doi = {10.5802/aif.1117},
     zbl = {0625.58040},
     mrnumber = {89e:16022},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1117/}
}
TY  - JOUR
AU  - Manin, Yu. I.
TI  - Some remarks on Koszul algebras and quantum groups
JO  - Annales de l'Institut Fourier
PY  - 1987
SP  - 191
EP  - 205
VL  - 37
IS  - 4
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1117/
DO  - 10.5802/aif.1117
LA  - en
ID  - AIF_1987__37_4_191_0
ER  - 
%0 Journal Article
%A Manin, Yu. I.
%T Some remarks on Koszul algebras and quantum groups
%J Annales de l'Institut Fourier
%D 1987
%P 191-205
%V 37
%N 4
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1117/
%R 10.5802/aif.1117
%G en
%F 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) no. 4, pp. 191-205. doi : 10.5802/aif.1117. https://aif.centre-mersenne.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

Cité par Sources :