Feigin homomorphisms map the ‘upper triangular subalgebras’ of quantum groups to some quantum (or twisted) polynomial algebras. They are important in the study of their skew fields of quotients. Several years ago, I gave a construction of these ‘quantum upper triangular subalgebras’ as subalgebras of quantum shuffle algebras. More recently, the construction of Feigin homomorphisms has been extended to the whole quantum shuffle algebras by D. Rupel, with a computational proof. I shall explain another, quite direct approach, stressing the universal property of the quantum shuffle algebra, and putting quantum polynomial algebras naturally in this framework. All necessary background will be recalled.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
