# On Fomin–Kirillov algebras for complex reflection groups

@article{Laugwitz2016OnFA,
title={On Fomin–Kirillov algebras for complex reflection groups},
author={Robert Laugwitz},
journal={Communications in Algebra},
year={2016},
volume={45},
pages={3653 - 3666}
}
ABSTRACT In this note, we apply classification results for finite-dimensional Nichols algebras 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…
3 Citations
On the dimension of the Fomin-Kirillov algebra and related algebras
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On the dimension of the Fomin-Kirillov algebra and related algebras
Let $\mathcal{E}_m$ be the Fomin-Kirillov algebra, and let $\mathcal{B}_{\mathbb{S}_m}$ be the Nichols-Woronowicz algebra model for Schubert calculus on the symmetric group $\mathbb{S}_m$ which is a
On the quadratic dual of the Fomin–Kirillov algebras
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<p>We study ring-theoretic and homological properties of the quadratic dual (or Koszul dual) <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"

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