In a previous work [AS2] we showed how to attach to a pointed Hopf algebra A with coradical kΓ, a braided strictly graded Hopf algebra R in the category Γ Γ YD of Yetter-Drinfeld modules over Γ. In this paper, we consider a further invariant of A, namely the subalgebra R of R generated by the space V of primitive elements. Algebras of this kind are known since the pioneering work of Nichols. It...

Abstract The Losev–Manin moduli space parametrizes pointed chains of projective lines. In this paper we study a possible generalization to families degenerate toric varieties. Geometric properties these families, such as flatness and reducedness the fibers, are explored via combinatorial characterization. We show that described by specific type polytope fibration which generalizes twisted Cayle...