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...

In this paper, some fundamental concepts are given relating to fuzzytopological spaces. Then it is shown that there is a contravariant functorfrom the category of the pointed fuzzy topological spaces to the category ofgroups and homomorphisms. Also the fuzzy topological spaces which are Hopfspaces are investigated and it is shown that a pointed fuzzy toplogicalspace having the same homotopy typ...

Let F be a finite extension of Q2, of degree d. Our first main theorem gives an explicit computation of the mod two homology Hopf algebra of the infinite general linear group GLF . The answer is formulated in terms of the well-known homology algebras of the infinite unitary group U, its classifying space BU, and the classifying space BO of the infinite orthogonal group. Let P denote the subalge...

In a previous work [AS2] we showed how to attach to a pointed Hopf algebra A with coradical kΓ, a braided strictly graded Hopf algebra R in the category Γ Γ YD of Yetter-Drinfeld modules over Γ. In this paper, we consider a further invariant of A, namely the subalgebra R of R generated by the space V of primitive elements. Algebras of this kind are known since the pioneering work of Nichols. It...

We introduce the Hopf algebra of uniform block permutations and show that it is self-dual, free, and cofree. These results are closely related to the fact that uniform block permutations form a factorizable inverse monoid. This Hopf algebra contains the Hopf algebra of permutations of Malvenuto and Reutenauer and the Hopf algebra of symmetric functions in non-commuting variables of Gebhard, Ros...

Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2 infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any realworld resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of ...