21 citations · 95 across the 33 of their papers we have counts for
9 papers · 1 filter
Cones from quantum groups to tropical flag varieties
Xin Fang, Ghislain Fourier, Markus Reineke
We relate quantum degree cones, parametrizing PBW degenerations of quantized enveloping algebras, to (negative tight monomial) cones introduced by Lusztig in the study of monomials…
Generalized virtual braid groups, quasi-shuffle product and quantum groups
Xin Fang
We introduce in this paper the generalized virtual braid group on n strands GVB_n, generalizing simultaneously the braid groups and their virtual versions. A Mastumoto-Tits type se…
Cofree Hopf algebras on Hopf bimodule algebras
Xin Fang, Run-Qiang Jian
We investigate a Hopf algebra structure on the cotensor coalgebra associated to a Hopf bimodule algebra which contains universal version of Clifford algebras and quantum groups as…
Non-symmetrizable quantum groups: defining ideals and specialization
Xin Fang
Two generating sets of the defining ideal of a Nichols algebra of diagonal type are proposed, which are then applied to study the bar involution and the specialization problem of q…
Multi-brace cotensor Hopf algebras and quantum groups
Xin Fang, Marc Rosso
We construct multi-brace cotensor Hopf algebras with bosonizations of quantum multi-brace algebras as examples. Quantum quasi-symmetric algebras are then obtained by taking particu…
A Borel-Weil-Bott type theorem of quantum shuffle algebras
Xin Fang
We prove in this paper a Borel-Weil-Bott type theorem for the coHochschild homology of a quantum shuffle algebra associated with quantum group datum taking coefficients in some wel…
Dedekind η-function and quantum groups
Xin Fang
We realize some powers of Dedekind -function as traces on quantum coordinate algebras.
On defining ideals and differential algebras of Nichols algebras
Xin Fang
This paper is devoted to understanding the defining ideal of a Nichols algebra from the decomposition of specific elements in the group algebra of braid groups. A family of primiti…
Quantum groups, q-Boson algebras and quantized Weyl algebras
Xin Fang
We give a unified construction of quantum groups, q-Boson algebras and quantized Weyl algebras and an action of quantum groups on quantized Weyl algebras. This enables us to give a…