Fibered quadratic Hopf algebras related to Schubert calculus
The paper is concerned with the study of a family of quadratic associative algebras \({\mathcal E}_n\) introduced by \textit{S. Fomin} and \textit{A. N. Kirillov} [Advances in geometry, Prog. Math. 172, 147-182 (1999; Zbl 0940.05070)]. A Hopf algebra structure is defined on the twisted group algebra \({\mathcal E}_n\{{\mathcal S}_n\}\), where \({\mathcal S}_n\) is the symmetric group. This structure is used to prove that \({\mathcal E}_n\) can be decomposed as a graded module into a tensor product, one of the tensor factors being \({\mathcal E}_{n-1}\).
scientific article; zbMATH DE number 1523169