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Titel:Deformed Fomin-Kirillov Algebras and Applications
Autor:Röhrig, Bastian
Weitere Beteiligte: Heckenberger, István (Prof. Dr.)
Veröffentlicht:2016
URI:https://archiv.ub.uni-marburg.de/diss/z2017/0049
URN: urn:nbn:de:hebis:04-z2017-00493
DOI: https://doi.org/10.17192/z2017.0049
DDC: Mathematik
Titel (trans.):Deformierte Fomin-Kirillov-Algebren und Anwendungen
Publikationsdatum:2017-01-12
Lizenz:https://rightsstatements.org/vocab/InC-NC/1.0/

Dokument

Schlagwörter:
Hopf-Algebra, Symmetrische Gruppe, Group, Mathematics, Nichols algebra, Gruppe <Mathematik>, Algebra, Nichols-Algebra, Algebra, symmetric group, Mathematik, Hopf algebra

Summary:
We consider a deformed version of Fomin-Kirillov algebras and investigate their relation to regular Fomin-Kirillov algebras. We observe that certain subalgebras of a deformed Fomin-Kirillov algebra closely resemble "smaller" Fomin-Kirillov algebras. This observation is used to calculate the vector space dimension of Fomin-Kirillov algebras in many examples, in particular for the complete graph on 5 vertices. Furthermore, we study groups attached to Fomin-Kirillov algebras. The attached groups turn out to posses striking structures in examples.

Bibliographie / References

  1. [BLM13] J. Blasiak, R.I. Liu, and K. Mesazros, Subalgebras of the FominKirillov algebra, Preprint arXiv:1310.4112 (2013), 38 pp.
  2. [Bou59] N. Bourbaki, Alegbre, ch. 9 , Eelments de mathematique, Hermann, Paris, 1959.
  3. [BHLGO15] H. Barnhielm, D. Holt, C.R. Leedham-Green, and E.A. O'Brien, A practical model for computation with matrix groups, Journal of Symbolic Computation 68 (2015), 27{60.
  4. [CCN+85] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of nite groups , Clarendon Press, Oxford, 1985.
  5. [FP00] S. Fomin and C. Procesi, Fibered quadratic Hopf algebras related to Schubert calculus, Journal of Algebra 230 (2000), 174{183.
  6. [Art44] E. Artin, Galois theory, 2nd edition, Notre Dame Math Lectures, no. 2., Notre Dame: University of Notre Dame, 1944.
  7. [Car56] R.D. Carmichael, Introduction to the theory of groups of nite order, Dover Publications, Inc., New York, 1956.
  8. [FLZ01] P. Fleischmann, W. Lempken, and A.E. Zalesskii, Linear groups over GF (2k) generated by a conjugacy class of a xed point free element of order 3, Journal of Algebra 244 (2001), 631{663.
  9. [AKM15] I. Angiono, M. Kochetov, and M. Mastnak, On rigidity of Nichols algebras, Journal of Pure and Applied Algebra 219 (2015), no. 12, 5539{5559.
  10. [BG96] A. Braverman and D. Gaitsgory, Poincaer-Birkho-Witt theorem for quadratic algebras of Koszul type, Journal of Algebra 181 (1996), no. 2, 315 { 328.
  11. [FK98] S. Fomin and A.N. Kirillov, Quadratic algebras, Dunkl elements, and Schubert calculus, Advances in Geometry and Mathematical Physics, Progr. Math., vol. 172, Birkhauser, 1998, pp. 147{182.
  12. [BCP97] W. Bosma, J. Cannon, and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997), 235{265.
  13. [GV16] M. Gran~a and L. Vendramin, Nichols algebras of non-abelian group type: zoo of examples , 2016. http://mate.dm.uba.ar/~lvendram/ zoo/
  14. [CK16] A.M. Cohen and J.W. Knopper, GBNP { a GAP package, Version 1.0.3, 2016. http://mathdox.org/gbnp/

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