Let K be a field of characteristic 0 containing all roots of unity. We classify the all Hopf structures on monomial K-coalgebras, or, in dual version, on monomial K-algebras.

We provide a quiver setting for quasi-Hopf algebras, generalizing the Hopf quiver theory. As applications we obtain some general structure theorems, in particular the quasi-Hopf analogue of theâ€¦ (More)

Let Uq(g) be the Drinfeld-Jimbo quantum group, which is a deformation of the universal enveloping algebra of a finite dimensional semisimple Lie algebra g. In the generic case, i.e. the parameter qâ€¦ (More)

We introduce the quiver of a bicomodule over a cosemisim-ple coalgebra. Applying this to the coradical C 0 of an arbitrary coalgebra C, we give an alternative definition of the Gabriel quiver of C,â€¦ (More)

We introduce the quiver of a bicomodule over a cosemisim-ple coalgebra. Applying this to the coradical C 0 of an arbitrary coalgebra C, we give an alternative definition of the Gabriel quiver of C,â€¦ (More)

By viewing Clifford algebras as algebras in some suitable symmetric Gr-categories, Albuquerque and Majid were able to give a new derivation of some well known results about Clifford algebras and toâ€¦ (More)

We introduce the quiver of a bicomodule over a cosemisim-ple coalgebra. Applying this to the coradical C 0 of an arbitrary coalgebra C, we give an alternative definition of the Gabriel quiver of C,â€¦ (More)

The doubling construction is a fast and important way to generate new solutions to the Hurwitz problem on sums of squares identities from any known ones. In this short note, we generalize theâ€¦ (More)

We study finite quasi-quantum groups in their quiver setting developed recently by the first author. We obtain a classification of finite-dimensional pointed Majid algebras of finite corepresentationâ€¦ (More)

A new two-dimensional (2D) carbon crystal, different from graphene, has been prepared from 1,3,5-trihydroxybenzene, consisting of 4-carbon and 6-carbon rings in 1:1 ratio, named 4-6 carbophene byâ€¦ (More)