Abstract
Let W be a Coxeter group. The goal of the paper is to construct new Hopf algebras that contain Hecke algebras Hq(W) as (left) coideal subalgebras. Our Hecke-Hopf algebras1H(W) have a number of applications. In particular they provide new solutions of quantum Yang-Baxter equation and lead to a construction of a new family of endo-functors of the category of Hq(W)-modules. Hecke-Hopf algebras for the symmetric group are related to Fomin-Kirillov algebras; for an arbitrary Coxeter group W the “Demazure” part of H(W) is being acted upon by generalized braided derivatives which generate the corresponding (generalized) Nichols algebra.
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