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}, mrnumber = {89e:16022}, zbl = {0625.58040}, language = {en}, url = {http://www.numdam.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 - http://www.numdam.org/articles/10.5802/aif.1117/ DO - 10.5802/aif.1117 LA - en ID - AIF_1987__37_4_191_0 ER -
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] Quantum groups, Zap. Naučn. sem. LOMI, vol. 155 (1986), 18-49 (in russian). | MR | Zbl
,[2] Koszul resolutions, Trans. AMS, 152-1 (1970), 39-60. | MR | Zbl
,[3] 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] Hopf algebras and vector-symmetries, Uspekhi Mat. Nauk, 41-5 (1986), 185-186 (in russian). | MR | Zbl
,[5] Tannakian categories, Springer lecture Notes in Math., vol. 900 (1982), 101-228. | MR | Zbl
, ,[6] Mixed categories, Ext-duality and representations, 1986, preprint.
, ,[7] 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 :