NON-AFFINE HOPF ALGEBRA DOMAINS OF GELFAND–KIRILLOV DIMENSION TWO
Glasgow mathematical journal, Tome 59 (2017) no. 3, pp. 563-593

Voir la notice de l'article provenant de la source Cambridge University Press

We classify all non-affine Hopf algebras H over an algebraically closed field k of characteristic zero that are integral domains of Gelfand–Kirillov dimension two and satisfy the condition Ext1 H (k, k) ≠ 0. The affine ones were classified by the authors in 2010 (Goodearl and Zhang, J. Algebra324 (2010), 3131–3168).
DOI : 10.1017/S0017089516000410
Mots-clés : 16T05, 57T05, 16P90, 16E65
GOODEARL, K. R.; ZHANG, J. J. NON-AFFINE HOPF ALGEBRA DOMAINS OF GELFAND–KIRILLOV DIMENSION TWO. Glasgow mathematical journal, Tome 59 (2017) no. 3, pp. 563-593. doi: 10.1017/S0017089516000410
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     journal = {Glasgow mathematical journal},
     pages = {563--593},
     year = {2017},
     volume = {59},
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000410/}
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[1] 1. Berstein, I., On the dimension of modules and algebras. IX. Direct limits, Nagoya Math. J. 13 (1958), 83–84. Google Scholar | DOI

[2] 2. Brown, K. A. and Gilmartin, P., Hopf algebras under finiteness conditions, Palest. J. Math. 3 (2014), 356–365, Special issue. Google Scholar

[3] 3. Brown, K. A., O'Hagan, S., Zhang, J. J. and Zhuang, G., Connected Hopf algebras and iterated Ore extensions, J. Pure Appl. Algebra, 219 (2015), 2405–2433. Google Scholar | DOI

[4] 4. Chirvasitu, A., Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebras, Algebra Number Theory 8 (5) (2014), 1179–1199. Google Scholar | DOI

[5] 5. Goodearl, K. R., Noetherian Hopf algebras, Glasg. Math. J. 55 (A) (2013), 75–87. Google Scholar | DOI

[6] 6. Goodearl, K. R. and Zhang, J. J., Noetherian Hopf algebra domains of Gelfand-Kirillov dimension two, J. Algebra 324 (2010), 3131–3168. Google Scholar | DOI

[7] 7. Gromov, M., Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53–73. Google Scholar | DOI

[8] 8. Huh, C. and Kim, C. O., Gelfand-Kirillov dimension of skew polynomial rings of automorphism type, Commun. Algebra 24 (1996), 2317–2323. Google Scholar | DOI

[9] 9. Lu, D.-M., Wu, Q.-S. and Zhang, J. J., Homological integral of Hopf algebras, Trans. Amer. Math. Soc. 359 (2007), 4945–4975. Google Scholar | DOI

[10] 10. Mcconnell, J. C. and Robson, J. C., Noncommutative noetherian rings (Wiley, Chichester, 1987). Google Scholar

[11] 11. Montgomery, S., Hopf algebras and their actions on rings, CBMS regional conference series in mathematics, vol. 82 (AMS, Providence, R1, 1993). Google Scholar | DOI

[12] 12. Nichols, W. D. and Zoeller, M. B., A Hopf algebra freeness theorem, Amer. J. Math. 111 (1989), 381–385. Google Scholar | DOI

[13] 13. Osofsky, B. L., Upper bounds on homological dimensions, Nagoya Math. J. 32 (1968), 315–322. Google Scholar | DOI

[14] 14. Panov, A. N., Ore extensions of Hopf algebras, Mat. Zametki 74 (2003), 425–434. Google Scholar

[15] 15. Radford, D. E., Operators on Hopf algebras, Amer. J. Math. 99 (1977), 139–158. Google Scholar | DOI

[16] 16. Radford, D. E., Pointed Hopf algebras are free over Hopf subalgebras, J. Algebra 45 (2) (1977), 266–273. Google Scholar | DOI

[17] 17. Schauenburg, P., Faithful flatness over Hopf subalgebras: Counterexamples, in Interactions between ring theory and representations of algebras (Murcia, Spain 1998) (F. Van Oystaeyen and M. Saorí n, Editors) (New York, Dekker, 2000), 331–344. Google Scholar

[18] 18. Skryabin, S., New results on the bijectivity of antipode of a Hopf algebra, J. Algebra 306 (2) (2006), 622–633. Google Scholar | DOI

[19] 19. Takeuchi, M., A correspondence between Hopf ideals and sub-Hopf algebras, Manuscripta Math. 7 (1972), 251–270. Google Scholar | DOI

[20] 20. Takeuchi, M., Relative Hopf modules–-Equivalences and freeness criteria, J. Algebra 60 (1979), 452–471. Google Scholar | DOI

[21] 21. Wang, D.-G., Zhang, J. J. and Zhuang, G., Hopf algebras of GK-dimension two with vanishing Ext-group, J. Algebra 388 (2013), 219–247. Google Scholar | DOI

[22] 22. Wang, D.-G., Zhang, J. J. and Zhuang, G., Lower bounds of growth of Hopf algebras, Trans. Amer. Math. Soc. 365 (9) (2013), 4963–4986. Google Scholar | DOI

[23] 23. Wang, D.-G., Zhang, J. J. and Zhuang, G., Primitive cohomology of Hopf algebras, J. Algebra 464 (2016), 36–96. Google Scholar | DOI

[24] 24. Wu, Q.-S. and Zhang, J. J., Noetherian PI Hopf algebras are Gorenstein, Trans. Amer. Math. Soc. 355 (2002), 1043–1066. Google Scholar | DOI

[25] 25. Zhuang, G., Properties of pointed and connected Hopf algebras of finite Gelfand-Kirillov dimension, J. London Math. Soc. (2) 87 (3) (2013), 877–898. Google Scholar | DOI

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