We introduce and study bimeasurings from pairs of bialge-bras to algebras. It is shown that the universal bimeasuring bialgebra construction, which arises from Sweedler's universal measuring coalgebra construction and generalizes the finite dual, gives rise to a contravariant functor on the category of bialgebras adjoint to itself. An interpretation of bimeasurings as algebras in the category o...

By improving the previous construction in [18] we observe that any reduced HNN extension is a corner of a certain reduced amalgamated free product in both the von Neumann algebra and the C∗-algebra settings. Then, the same fact is shown for universal HNN extensions of C∗-algebras. We apply the observation to the questions of factoriality and type classification of HNN extensions of von Neumann ...

We analyze the algebraic structures of G–Frobenius algebras which are the algebras associated to global group quotient objects. Here G is any finite group. These algebras turn out to be modules over the Drinfeld double of the group ring k[G]. We furthermore prove that discrete torsion is a universal group action of H(G, k∗) on G–Frobenius algebras by isomorphisms of the underlying linear struct...

It was proposed that the Calabi-Yau geometry can be intrinsically connected with some new symmetries, some new algebras. In order to do this it has been analyzed the graphs constructed from K3-fibre CYd (d ≥ 3) reflexive polyhedra. The graphs can be naturally get in the frames of Universal Calabi-Yau algebra (UCYA) and may be decode by universal way with the changing of some restrictions on the...

A universal quasitriangular R–matrix for the non-standard quantum (1+1) Poincaré algebra Uziso(1, 1) is deduced by imposing analyticity in the deformation parameter z. A family gμ of “quantum graded contractions” of the algebra Uziso(1, 1)⊕U−ziso(1, 1) is obtained; this set of quantum algebras contains as Hopf subalgebras with two primitive translations quantum analogues of the two dimensional ...

Rota-Baxter algebras appeared in both the physics and mathematics literature. It is of great interest to have a simple construction of the free object of this algebraic structure. For example, free commutative Rota-Baxter algebras relate to double shuffle relations for multiple zeta values. The interest in the non-commutative setting arose in connection with the work of Connes and Kreimer on th...

The purpose of this paper is to study Sabinin algebras Hom-type. It shown that Lie, Malcev, Bol and other Hom-type are naturally To end, we provide a general key construction establish relationship between identities some class Hom-algebras ordinary algebras. Moreover, discuss new concept Hom-bialgebra, in relation with universal enveloping Hom-algebras. A based on primitive elements provided.

The Connes-Kreimer renormalization Hopf algebras are examples of a canonical quantization procedure for pre-Lie algebras. We give a simple construction and explanation of this quantization using the universal enveloping algebra for so-called twisted Lie algebras (Lie algebras in the category of symmetric sequences of k-modules). As an application, we obtain a simple proof of the (strengthened) ...

We deene process algebras with a generalised operation P for choice. For every innnite cardinal , we prove that the algebra of transition trees with branching degree < is free in the class of process algebras in which P is deened for all subsets with a cardinality <. We explain how the expressions of a fragment of the speciication language CRL may be used to denote elements of our process algeb...