Finite dimensional Nichols algebras of diagonal type over fields of positive characteristic

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.

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Bibliographic Details
Main Author: Wang, Jing
Contributors: Heckenberger, Istvan (Prof.Dr.) (Thesis advisor)
Format: Dissertation
Language:English
Published: Philipps-Universität Marburg 2016
Reine und Angewandte Mathematik
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1. 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)


2. Andruskiewitsch, N.: On nite-dimensional Hopf algebras. Proceedings of the International Congress of Mathematicians, Seoul 2014. Vol II (2014), 117-141.


3. Andruskiewitsch, N. and Graña, M.: Braided Hopf algebras over non-abelian nite groups. Bol. Acad. Nac. Cienc. (Córdoba). 63 (1999), 45-78.


4. 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.


5. 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.


6. Andruskiewitsch, N. and Schneider, H.-J.: Finite quantum groups and Cartan matrices. Adv. Math. 154 (2000), 1-45.


7. 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)


8. Andruskiewitsch, N. and Schneider, H.-J.: On the classi cation of nite- dimensional pointed Hopf algebras. Ann. Math. 171 (2010), 375-417.


9. Angiono, I.: On Nichols algebras of diagonal type. J. Reine Angew. Math. 683 (2013), 189-251.


10. 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.


11. 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.


12. Cuntz, M. and Heckenberger, I.: Weyl groupoids of rank two and continued fractions, Algebra and Number Theory, 3 (2009), no. 3, 317-340.


13. Cuntz, M. and Heckenberger, I: Weyl groupoids with at most three objects. Journal of pure and applied algebra 213 (2009), no. 6, 1112-1128.


14. 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.


15. Cuntz, M. and Heckenberger, I: Finite Weyl groupoids of rank three. Transac- tions of the American Mathematical Society 364 (2012), no. 3, 1369-1393.


16. 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.


17. Grana, M.: A freeness theorem for Nichols Algebras. J. Algebra. 231(1) (2000), 235-257.


18. Heckenberger, I.: Finite dimensional rank 2 Nichols algebras of diagonal type. I: Examples. Preprint math.QA/0402350


19. Heckenberger, I.: Finite dimensional rank 2 Nichols algebras of diagonal type. II: Classi cation. Preprint math.QA/0404008


20. Heckenberger, I.: Weyl equivalence for rank 2 Nichols algebras of diagonal type. Ann. Uni. Ferrara, 51(1) (2005), 281-289.


21. Heckenberger, I.: Classi cation of arithmetic root systems of rank 3. Actas del "XVI Coloquio Latinoamericano de Álgebra" 227-252(2005)


22. Heckenberger, I.: The Weyl groupoid of a Nichols algebra of diagonal type, Invent. Math. 164 (2006), 175-188.


23. Heckenberger, I.: Examples of nite-dimensional rank 2 Nichols algebras of diagonal type. Compositio Math. 143(1) (2007), 165-190.


24. Heckenberger, I.: Rank 2 Nichols algebras with nite arithmetic root system. Algebra and Representation Theory 11 (2008), 115-132.


25. Heckenberger, I.: Classi cation of arithmetic root systems. Adv. Math. 220 (2009), 59--124.


26. Heckenberger, I. and Schneider, H.-J.: Root systems and Weyl groupoids for Nichols algebras. Proc. Lond. Math. Soc. 101 (2010), no. 3, 623-654.


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. 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.


29. Heckenberger, I. and Yamane, H.: A generalization of Coxeter groups, root systems, and Matsumoto's theorem, Math. Z. 259 (2008), 255-276.


30. Kac, V.G.: In nite dimensional Lie algebras. Cambridge Univ. Press (1990).


31. Kharchenko, V.: A quantum analog of the Poincaré-Birkho -Witt theorem, Algebra and Logic, 38(4) (1999), 259-276.


32. Lusztig, G.: Introduction to Quantum Groups. Modern Birkhäuser Classics. Birkhäuser/Springer, New York, (2010). Reprint of the 1994 edition.


33. 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.


34. Nichols, W.D.: Bialgebras of type one. Commun. Alg. 6 (1978), 1521-1552. 96 B


35. Rosso, M.: Quantum groups and quantum shu es. Invent. Math. 133 (1998), 399-416.


36. Schauenburg, P.: A characterization of the Borel-like subalgebras of quantum enveloping algebras. Commun. Algebra. 24 (1996), 2811-2823.


37. 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.


38. Semikhatov, A.M. and Tipunin, I.Yu.: The Nichols algebra of screenings. Com- mun. Contemp. Math. 14 (2012)


39. Semikhatov, A.M. and Tipunin, I.Yu.: Logarithmic s (2) CFT models from Nichols algebras. I. J. Phys. A46 (2013)


40. Takeuchi, M.: Survey of braided Hopf algebras Contemp. Math., 267(2000),301-323


41. Woronowicz, S.L.: Compact matrix pseudogroups. Comm. Math. Phys. 111(4) (1987), 613-665.


42. Woronowicz, S.L.: Di erential calculus on compact matrix pseudogroups (quantum groups). Comm. Math. Phys. 122(1) (1989), 125-170.


43. Mar.2014 Colloquium on Algebra and Representations -Santa Maria, Brazil-Quantum 14


44. Apr.2011 -Zhejiang University, Hangzhou, China Nov.2011 Left symmetric algebras from DNA insertion Supported by ZJNSF(No.Y6100148, Y610027) and Education Department of Zhejiang Province(No.201019063).