We consider a generalization of the representation of the so-called co-Minkowski plane (due to H. and R. Struve) to an abelian group (V;+) and a commutative subgroup G of Aut(V;+). If P = G × V satis7es suitable conditions then an invariant re8ection structure (in the sense of Karzel (Discrete Math. 208=209 (1999) 387–409)) can be introduced in P which carries the algebraic structure of K-loop ...

A Lie version of Turaev’s G-Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a g-quasi-Frobenius Lie algebra for g a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra (q, β) together with a left g-module structure which acts on q via derivations and for which β is g-inva...

In §1 we use COO-vector methods, essentially Frobenius reciprocity, to derive the Howe-Richardson multiplicity formula for compact nilmanifolds. In §2 we use Frobenius reciprocity to generalize and considerably simplify a reduction procedure developed by Howe for solvable groups to general extensions of nilpotent Lie groups. In §3 we give an application of the previous results to obtain a reduc...

We present a universal construction of almost duality for Frobenius manifolds. The analytic setup of this construction is described in details for the case of semisimple Frobenius manifolds. We illustrate the general considerations by examples from the singularity theory, mirror symmetry, the theory of Coxeter groups and Shephard groups, from the Seiberg Witten duality.

Frobenius groups are an object of fundamental importance in finite group theory. As such, several generalizations these have been considered. Some examples include: A Frobenius–Wielandt is a triple ( G , H L ) where / almost complement for ; Camina pair N kernel M and pairs. In this paper we study triples groups.

Frobenius is generally considered the creator of character theory finite groups. This achievement came from study group determinant, which determinant a matrix coming regular representation. We generalize several Frobenius’ results about and use them to find new formulation supercharacter in terms factorizations determinant.

we give a new proof of the well known wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎we apply the concept of frobenius kernel in frobenius representation theorem in finite group‎ ‎theory to build a proof‎.