Given a nite graded poset with labeled Hasse diagram, we construct a quasi-symmetric generating function for chains whose labels have xed descents. This is a common generalization of a generating function for the ag f-vector de-ned by Ehrenborg and of a symmetric function associated to certain edge-labeled posets which arose in the theory of Schubert polynomials. We show this construction gives...

The subject of this paper are two Hopf algebras which are the non-commutative analogues of two different groups of formal power series. The first group is the set of invertible series with the group law being multiplication of series, while the second group is the set of formal diffeomorphisms with the group law being composition of series. The motivation to introduce these Hopf algebras comes ...

Since the Connes–Kreimer Hopf algebra was proposed, revisiting present quantum field theory has become meaningful and important from algebraic points. In this paper, the Hopf algebra in the cutting rules is constructed. Its coproduct contains all necessary ingredients for the cutting equation crucial to proving the perturbative unitarity of the S-matrix. Its antipode is compatible with the caus...

We give a rigorous proof that the (codimension one) Connes-Moscovici Hopf algebra HCM is isomorphic to a bicrossproduct Hopf algebra linked to a group factorisation of the diffeomorphism group Diff(R). We construct a second bicrossproduct UCM equipped with a nondegenerate dual pairing with HCM. We give a natural quotient Hopf algebra kλ[Heis] of HCM and Hopf subalgebra Uλ(heis) of UCM which aga...

This paper is the continuation of section 2 of the paper ”Floating bundles and their applications” [1]. Let (H, μ, η,∆, ε, S) be a commutative Hopf algebra over ring R without torsion and F(x ⊗ 1, 1⊗ x) be a formal group over Hopf algebra H. By HQ denote the Hopf algebra H⊗ Z Q over ring RQ = R⊗ Z Q. We shall write μ, η, . . . instead of μQ, ηQ, . . . . The aim of this paper is to prove the fol...

Hopf algebra structures on the extended q-superplane and its differential algebra are defined. An algebra of forms which is obtained from the generators of the extended q-superplane is introduced and its Hopf algebra structure is given. E-mail: [email protected] New E-mail address: [email protected]

We study ideals in Hall algebras of monoid representations on pointed sets corresponding to certain conditions on the representations. These conditions include the property that the monoid act via partial permutations, that the representation possess a compatible grading, and conditions on the support of the module. Quotients by these ideals lead to combinatorial Hopf algebras which can be inte...

The main goal of this paper is to investigate the structure of Hopf algebras with the property that either its Jacobson radical is a Hopf ideal or its coradical is a subalgebra. In order to do that we define the Hochschild cohomology of an algebra in an abelian monoidal category. Then we characterize those algebras which have dimension less than or equal to 1 with respect to Hochschild cohomolo...

We introduce the notion of 'bar category' by which we mean a monoidal category equipped with additional structure induced by complex conjugation. Examples of our theory include bimodules over a *-algebra, modules over a conventional Hopf *-algebra and modules over a more general object which call a 'quasi-*-Hopf algebra' and for which examples include the standard quantum groups u q (g) at q a ...

Let A and B be two Hopf algebras and R ∈ Hom(B ⊗ A, A ⊗ B), the twisted tensor product Hopf algebra A#RB was introduced by S. Caenepeel et al in [3] and further studied in our recent work [6]. In this paper we give the necessary and sufficient conditions for A#RB to be a Hopf algebra with a projection. Furthermore, a braided Hopf algebra A is constructed by twisting the multiplication of A thro...