Some remarks on Koszul algebras and quantum groups

Yu. I. Manin

Annales de l'institut Fourier (1987)

  • Volume: 37, Issue: 4, page 191-205
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Manin, Yu. I.. "Some remarks on Koszul algebras and quantum groups." Annales de l'institut Fourier 37.4 (1987): 191-205. <http://eudml.org/doc/74774>.

@article{Manin1987,
abstract = {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.},
author = {Manin, Yu. I.},
journal = {Annales de l'institut Fourier},
keywords = {category of quadratic algebras; tensor structure; Hopf algebras; quantum groups; Koszul algebras; Yang-Baxter equation},
language = {eng},
number = {4},
pages = {191-205},
publisher = {Association des Annales de l'Institut Fourier},
title = {Some remarks on Koszul algebras and quantum groups},
url = {http://eudml.org/doc/74774},
volume = {37},
year = {1987},
}

TY - JOUR
AU - Manin, Yu. I.
TI - Some remarks on Koszul algebras and quantum groups
JO - Annales de l'institut Fourier
PY - 1987
PB - Association des Annales de l'Institut Fourier
VL - 37
IS - 4
SP - 191
EP - 205
AB - 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.
LA - eng
KW - category of quadratic algebras; tensor structure; Hopf algebras; quantum groups; Koszul algebras; Yang-Baxter equation
UR - http://eudml.org/doc/74774
ER -

References

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  1. [1] V. G. DRINFELD, Quantum groups, Zap. Naučn. sem. LOMI, vol. 155 (1986), 18-49 (in russian). Zbl0617.16004MR88f:17017
  2. [2] S. B. PRIDDY, Koszul resolutions, Trans. AMS, 152-1 (1970), 39-60. Zbl0261.18016MR42 #346
  3. [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. Zbl0595.16020MR88f:16030
  4. [4] V. V. LYUBASHENKO, Hopf algebras and vector-symmetries, Uspekhi Mat. Nauk, 41-5 (1986), 185-186 (in russian). Zbl0649.16008MR88c:58007
  5. [5] P. DELIGNE, J. MILNE, Tannakian categories, Springer lecture Notes in Math., vol. 900 (1982), 101-228. Zbl0477.14004MR84m:14046
  6. [6] A. A. BEILINSON, V. GINSBURG, Mixed categories, Ext-duality and representations, 1986, preprint. 
  7. [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). Zbl0783.58025MR89c:58048

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