Publikationsserver der Universitätsbibliothek Marburg

Titel:Finite dimensional Nichols algebras of diagonal type over fields of positive characteristic
Autor:Wang, Jing
Weitere Beteiligte: Heckenberger, Istvan (Prof.Dr.)
Veröffentlicht:2016
URI:https://archiv.ub.uni-marburg.de/diss/z2016/0480
URN: urn:nbn:de:hebis:04-z2016-04806
DOI: https://doi.org/10.17192/z2016.0480
DDC: Mathematik
Titel (trans.):Endlich-dimensionale Nichols-Algebren von Diagonalem Typ über Körpern von positiver Charakteristik
Publikationsdatum:2016-08-24
Lizenz:https://creativecommons.org/licenses/by/4.0

Dokument

Schlagwörter:
Cartan-Graph, Weyl groupoid, Hopf algebra, Nichols-Algebra, Cartan graph, Hopf-Algebra, das Wurzelsystem, Nichols algebra, Weyl-Gruppoid, root system

Summary:
In this thesis we classify the rank 2 and rank 3 Nichols algebras of diagonal type with a finite root system over fields of positive characteristic.

Bibliographie / References

  1. Cuntz, M. and Heckenberger I., Re ection groupoids of rank two and Cluster algebras of type A, Combin. Theory Ser. A. 118 (2011), no. 4, 1350-1363. arXiv: 0911.3051.
  2. Andruskiewitsch, N.: About nite dimensional Hopf algebras. In Quantum symmetries in theoretical physics and mathematics (Bariloche, 2000), vol. 294 ser. Contemp. Math., pp. 1-57. Amer. Math. Soc. (2002)
  3. Schauenburg, P.: A characterization of the Borel-like subalgebras of quantum enveloping algebras. Commun. Algebra. 24 (1996), 2811-2823.
  4. Grana, M.: A freeness theorem for Nichols Algebras. J. Algebra. 231(1) (2000), 235-257.
  5. Heckenberger, I. and Yamane, H.: A generalization of Coxeter groups, root systems, and Matsumoto's theorem, Math. Z. 259 (2008), 255-276.
  6. Gaberdiel, M.R.: An algebraic approach to logarithmic conformal eld theory. In Proceedings of the School and Workshop on Logarithmic Conformal Field Theory and its Applications (Tehran, 2001). 18 (2003), 4593-4638.
  7. Angiono, I.: A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems. J. Europ. Math. Soc. 17 (2015), 2643-2671.
  8. Kharchenko, V.: A quantum analog of the Poincaré-Birkho -Witt theorem, Algebra and Logic, 38(4) (1999), 259-276.
  9. Nichols, W.D.: Bialgebras of type one. Commun. Alg. 6 (1978), 1521-1552. 96 B
  10. Andruskiewitsch, N. and Graña, M.: Braided Hopf algebras over non-abelian nite groups. Bol. Acad. Nac. Cienc. (Córdoba). 63 (1999), 45-78.
  11. Heckenberger, I.: Classi cation of arithmetic root systems. Adv. Math. 220 (2009), 59--124.
  12. Heckenberger, I.: Classi cation of arithmetic root systems of rank 3. Actas del "XVI Coloquio Latinoamericano de Álgebra" 227-252(2005)
  13. Mar.2014 Colloquium on Algebra and Representations -Santa Maria, Brazil-Quantum 14
  14. Woronowicz, S.L.: Compact matrix pseudogroups. Comm. Math. Phys. 111(4) (1987), 613-665.
  15. Woronowicz, S.L.: Di erential calculus on compact matrix pseudogroups (quantum groups). Comm. Math. Phys. 122(1) (1989), 125-170.
  16. Heckenberger, I.: Examples of nite-dimensional rank 2 Nichols algebras of diagonal type. Compositio Math. 143(1) (2007), 165-190.
  17. Heckenberger, I.: Finite dimensional rank 2 Nichols algebras of diagonal type. I: Examples. Preprint math.QA/0402350
  18. Heckenberger, I.: Finite dimensional rank 2 Nichols algebras of diagonal type. II: Classi cation. Preprint math.QA/0404008
  19. Andruskiewitsch, N. and Schneider, H.-J.: Finite quantum groups and Cartan matrices. Adv. Math. 154 (2000), 1-45.
  20. Cibils, C. and Lauve, A. and Witherspoon, S.: Hopf quivers and Nichols al- gebras in positive characteristic. Proc. Amer. Math. Soc. 137 (2009), no. 12, 4029-4041.
  21. Cuntz, M. and Heckenberger, I: Finite Weyl groupoids of rank three. Transac- tions of the American Mathematical Society 364 (2012), no. 3, 1369-1393.
  22. Kac, V.G.: In nite dimensional Lie algebras. Cambridge Univ. Press (1990).
  23. Lusztig, G.: Introduction to Quantum Groups. Modern Birkhäuser Classics. Birkhäuser/Springer, New York, (2010). Reprint of the 1994 edition.
  24. Andruskiewitsch, N. and Schneider, H.-J.: Lifting of quantum linear spaces and pointed Hopf algebras of order p 3 . J. Algebra. 209 (1998), 658-691.
  25. Semikhatov, A.M. and Tipunin, I.Yu.: Logarithmic s (2) CFT models from Nichols algebras. I. J. Phys. A46 (2013)
  26. Semikhatov, A.M: Virasoro central charges for Nichols algebras. Conformal Field Theories and Tensor Categories: Proceedings of a Workshop held at Bei- jing international center for mathematical research.
  27. Heckenberger, I. and Schneider, H.-J.: Nichols algebras over groups with nite root system of rank two I. J. Algebra. 324 (2010), no. 11, 3090-3114.
  28. Majid, S.: Noncommutative di erentials and Yang-Mills on permutation groups S n . In Hopf algebras in noncommutative geometry and physics, vol- ume 239 of Lecture Notes in Pure and Appl. Math. (2005), 189-213.
  29. Angiono, I.: On Nichols algebras of diagonal type. J. Reine Angew. Math. 683 (2013), 189-251.
  30. Andruskiewitsch, N.: On nite-dimensional Hopf algebras. Proceedings of the International Congress of Mathematicians, Seoul 2014. Vol II (2014), 117-141.
  31. Andruskiewitsch, N. and Schneider, H.-J.: On the classi cation of nite- dimensional pointed Hopf algebras. Ann. Math. 171 (2010), 375-417.
  32. Andruskiewitsch, N. and Schneider, H.-J.: Pointed Hopf algebras. In New Di- rections in Hopf Algebras, vol. 43 ser. MSRI Publications. Cambridge University Press (2002)
  33. Rosso, M.: Quantum groups and quantum shu es. Invent. Math. 133 (1998), 399-416.
  34. Heckenberger, I.: Rank 2 Nichols algebras with nite arithmetic root system. Algebra and Representation Theory 11 (2008), 115-132.
  35. Heckenberger, I. and Schneider, H.-J.: Right coideal subalgebras of Nichols al- gebras and the Du o order on the Weyl groupoid. Israel Journal of Mathemat- ics. 197 (2013), 139--187.
  36. Heckenberger, I. and Schneider, H.-J.: Root systems and Weyl groupoids for Nichols algebras. Proc. Lond. Math. Soc. 101 (2010), no. 3, 623-654.
  37. Takeuchi, M.: Survey of braided Hopf algebras Contemp. Math., 267(2000),301-323
  38. Andruskiewitsch, N. and Heckenberger, I. and Schneider, H.-J.: The Nichols algebra of a semisimple Yetter-Drinfeld module. Amer. J. Math. 132 (2010) no. 6 1493-1547.
  39. Semikhatov, A.M. and Tipunin, I.Yu.: The Nichols algebra of screenings. Com- mun. Contemp. Math. 14 (2012)
  40. Heckenberger, I.: The Weyl groupoid of a Nichols algebra of diagonal type, Invent. Math. 164 (2006), 175-188.
  41. Heckenberger, I.: Weyl equivalence for rank 2 Nichols algebras of diagonal type. Ann. Uni. Ferrara, 51(1) (2005), 281-289.
  42. Cuntz, M. and Heckenberger, I.: Weyl groupoids of rank two and continued fractions, Algebra and Number Theory, 3 (2009), no. 3, 317-340.
  43. Cuntz, M. and Heckenberger, I: Weyl groupoids with at most three objects. Journal of pure and applied algebra 213 (2009), no. 6, 1112-1128.


* Das Dokument ist im Internet frei zugänglich - Hinweise zu den Nutzungsrechten