In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.

The Turaev-Viro state sum invariant can be extended to 3-manifolds with free boundaries. We use this fact describe generalized Frobenius-Schur indicators as invariants of solid tori. This provides a geometric understanding the $\mathrm{SL}(2,\mathbb{Z})$-equivariance these indicators.

An (association) scheme is said to be Frobenius if it the (orbital) of a group. A which has same tensor intersection numbers as some pseudofrobenius. We establish necessary and sufficient condition for an imprimitive pseudofrobenius Frobenius. also prove strong conditions existence not As byproduct, we obtain group G with abelian kernel determined up isomorphism only by character table G. Final...

A short and simple derivation of the formula of Frobenius, which gives the dimensions of the irreducible representations of S(n), the symmetric group on any number, n, of symbols, is given. These dimensions are the characters of the identity element of the group, i.e., of the element all of whose cycles are unary. It is shown how a slight modification of Frobenius' formula yields, when n = 2p i...

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 study quasi-Hopf algebras and their subobjects over certain commutative rings from the point of view of Frobenius algebras. We introduce a type of Radford formula involving an anti-automorphism and the Nakayama automorphism of a Frobenius algebra, then view several results in quantum algebras from this vantage-point. In addition, separability and strong separability of quasi-Hopf algebras ar...