Using the a noncommutative version of Chevalley’s theorem due to Bergeron, Reutenauer, Rosas, and Zabrocki we compute the graded Frobenius series for their two sets of noncommutative harmonics with respect to the left action of the symmetric group (acting on variables). We use these results to derive the Frobenius series for the enveloping algebra of the derived free Lie algebra in n variables....

The notion of a Frobenius coring is introduced, and it is shown that any such coring produces a tower of Frobenius corings and Frobenius extensions.

Recapitulation The origin of the representation theory of finite groups can be traced back to a correspondence between R. Dedekind and F. G. Frobenius that took place in April of 1896. The present article is based on several lectures given by the author in 1996 in commemoration of the centennial of this occasion. In Part I of this article we recounted the story of how Dedekind proposed to Frobe...

We prove the Kobayashi-Hitchin correspondence between good wild harmonic bundles and polystable filtered $\lambda$-flat satisfying a vanishing condition. also study for with homogeneity respect to group action, which is expected provide another way construct Frobenius manifolds.

Based on the Frobenius series method, stresses analysis of the functionally graded rotating thick cylindrical pressure vessels (FGRTCPV) are examined. The vessel is considered in both plane stress and plane strain conditions. All of the cylindrical shell properties except the Poisson ratio are considered exponential function along the radial direction. The governing Navier equation for this pro...

We study co-Frobenius and more generally Quasi-co-Frobenius corings over arbitrary baserings and over PF baserings in particular. We generalize some results about (Quasi-) co-Frobenius coalgebras to the case of non-commutative base rings and give several new characterisations for co-Frobenius and Quasi-co-Frobenius corings, some of them are new even in the coalgebra situation. We construct Mori...

It is well-known that the value of Frobenius–Schur indicator $$|G|^{-1} \sum _{g\in G} \chi (g^2)=\pm 1$$ a real irreducible representation finite group G determines which two types representations it belongs to, i.e. whether strictly or quaternionic. We study extension to case when homomorphism $$\varphi :G\rightarrow \mathbb {Z}/2\mathbb {Z}$$ gives algebra $$\mathbb {C}[G]$$ structure supera...

Given a Laurent polynomial over flat $$\mathbf {Z}$$ -algebra, Vlasenko defines formal group law. We identify this law with coordinate system of functor. When the “Hasse–Witt matrix” is invertible, matrix by taking certain $$p$$ -adic limit. show that Frobenius Dieudonné module modulo .

We begin with personal notes describing the atmosphere of ”Bogoliubov renormalization group” birth. Then we expose the history of RG discovery in the QFT and of the RG method devising in the mid-fifties. The third part is devoted to proliferation of RG ideas into diverse parts of theoretical physics. We conclude with discussing the perspective of RG method further development and its applicatio...

We give an example of an infinite simple Frobenius group G without involutions, with a trivial kernel and a nilpotent complement. Nevertheless, this group is not ωstable (not even superstable), this is the ”only” property missing in order to be a counterexample to the Cherlin-Zil’ber Conjecture which says that simple ωstable groups are algebraic groups.