The final goal of this paper is to introduce certain finite dimensional Hopf algebras associated with restricted Frobenius Lie algebras over a field of characteristic p > 0. The antipodes of these Hopf algebras have order either 2p or 2, and in the minimal dimension p there exists just one Hopf algebra in this class which coincides with an example due to Radford [35] of a Hopf algebra with a no...

Braided Hopf algebras have attracted much attention in both mathematics and mathematical physics (see e.g. [2][4][14][16][17][18][20][23]). The classification of finite dimensional Hopf algebras is interesting and important for their applications (see [1] [24]). Braided Hopf algebras play an important role in the classification of finite-dimensional pointed Hopf algebras (e.g. [1][2] [21]). The...

The present work will focus on a Kaldor-Kalecki non –linear business cycle model in income and capital, with discrete time and delay argument characteristics. What it will state, considering an investment function similar to the one proposed by Rodano and using the linear approximation analysis, are the local stability property and local bifurcations conditions, given the parameter space. Numer...

The quiver Hopf algebras are classified by means of ramification system with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Hopf algebras of type one. 2000 Mathematics Subject Classification: 16W30, 16G10 keywords: Quiver, Hopf algebra, Hopf bimodule, Nichols algebras

In this note we study logarithmic transformations in the sense of differential topology on two fibers of the Hopf surface. It is known that such transformations are susceptible to yield exotic smooth structures on four-manifolds. We will show here that this is not the case for the Hopf surface, all integer homology Hopf surfaces we obtain are diffeomorphic to the standard Hopf surface.

We propose a new type of Hopf semimetals indexed by a pair of numbers (p, q), where the Hopf number is given by pq. The Fermi surface is given by the preimage of the Hopf map, which consists of loops nontrivially linked for a nonzero Hopf number. The Fermi surface forms a torus link, whose examples are the Hopf link indexed by (1, 1), the Solomon’s knot (2, 1), the double Hopf-link (2, 2) and t...

The quiver Hopf algebras are classified by means of ramification system with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Nichols type Hopf algebras. 2000 Mathematics Subject Classification: 16W30, 16G10 keywords: Quiver, Hopf algebra, Hopf bimodule, Nichols algebras

We study the self-dual Hopf algebra HSP of special posets introduced by Malvenuto and Reutenauer and the Hopf algebra morphism from HSP to the Hopf algebra of free quasi-symmetric functions FQSym given by linear extensions. In particular, we construct two Hopf subalgebras both isomorphic to FQSym; the first one is based on plane posets, the second one on heap-ordered forests. An explicit isomor...

We notice that for a Hopf algebra H , its antipode S is both an epimorphism and a monomorphism from H to H in the category of Hopf algebras over a field. Together with the existence of Hopf algebras with non-injective or non-surjective antipode, this proves the existence of non-surjective epimorphisms and non-injective monomorphisms in the category of Hopf algebras. Using Schauenburg’s free Hop...

Cyclic cohomology of Hopf algebras admitting a modular pair was first defined in [2] and further developed in [3] and [4] in the context of transverse geometry. Their results are followed by several papers computing Hopf cyclic (co)homology of certain Hopf algebras such as [15], [5] and [13]. In a series of papers [1], [10], [11], and [6] the authors developed a theory of cyclic (co)homology wh...