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On Fomin--Kirillov Algebras for Complex Reflection Groups | | Robert Laugwitz
; | | Date: |
1 May 2016 | | Abstract: | This note is an application of classification results for finite-dimensional
Nichols algebras over groups. We apply these results to generalizations of
Fomin--Kirillov algebras to complex reflection groups. First, we focus on the
case of cyclic groups where the corresponding Nichols algebras are only
finite-dimensional up to order four, and we include results about the existence
of Weyl groupoids and finite-dimensional Nichols subalgebras for this class.
Second, recent results by Heckenberger--Vendramin [ArXiv e-prints, 1412.0857
(December 2014)] on the classification of Nichols algebras of semisimple group
type can be used to find that these algebras are infinite-dimensional for many
non-exceptional complex reflection groups in the Shephard--Todd classification. | | Source: | arXiv, 1605.0227 | | Services: | Forum | Review | PDF | Favorites | |
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