Root Systems In Finite Symplectic Vector Spaces

@article{Lentner2013RootSI,
  title={Root Systems In Finite Symplectic Vector Spaces},
  author={Simon D. Lentner},
  journal={Communications in Algebra},
  year={2013},
  volume={43},
  pages={4446 - 4470}
}
  • Simon D. Lentner
  • Published 2013
  • Mathematics
  • Communications in Algebra
  • We study realizations of root systems in possibly degenerate symplectic vector spaces over finite fields, up to symplectic isomorphisms. The main result of this article is the classification of such realizations for the field 𝔽2. Thereby, each root system requires a specific degree of degeneracy of the symplectic vector space. Our main motivation for this article is that for each such realization of a root system we can construct a Nichols algebra over a nonabelian group. 
    Factorization of Graded Traces on Nichols Algebras
    1

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