We define certain extensions of Jacobi groups A<sub>1</sub>, prove an analogue Chevalley theorem for their invariants, and construct a Dubrovin-Frobenius structure on its orbit space.

In the present paper, we study the cuspidalization problem for fundamental groups of configuration spaces of proper hyperbolic curves over finite fields. The goal of this paper is to show that any Frobenius-preserving isomorphism of the geometrically pro-l fundamental groups of hyperbolic curves induces an isomorphism of the geometrically pro-l fundamental groups of the associated configuration...

We analyze the algebraic structures of G–Frobenius algebras which are the algebras associated to global group quotient objects. Here G is any finite group. These algebras turn out to be modules over the Drinfeld double of the group ring k[G]. We furthermore prove that discrete torsion is a universal group action of H(G, k∗) on G–Frobenius algebras by isomorphisms of the underlying linear struct...

Frobenius bimodules are connected with Frobenius algebras and extensions. For instance, a ring extension φ : R → S is a Frobenius extension if and only if RSS is a Frobenius bimodule [1]. Brzeziński and Gómez-Torrecillas studied in [4] certain properties of comatrix corings in relation to properties of bimodules. In particular they showed that the comatrix coring [6] induced by any Frobenius bi...