609 research outputs found
The fundamental group of a Hopf linear category
We define the fundamental group of a Hopf algebra over a field. For this
purpose we first consider gradings of Hopf algebras and Galois coverings. The
latter are given by linear categories with new additional structure which we
call Hopf linear categories over a finite group. We compare this invariant to
the fundamental group of the underlying linear category, and we compute those
groups for families of examples.Comment: Computations of the fundamental group of some Hopf algebras are
added. The relation with the fundamental group of the underlying associative
structure is now considered. We also analyse the situation when universal
covers and/or gradings exist. Dedicated to Eduardo N. Marcos for his 60th
birthday. 24 page
On the classification and properties of noncommutative duplicates
We give an explicit description of the set of all factorization structures,
or twisting maps, existing between the algebras k^2 and k^2, and classify the
resulting algebras up to isomorphism. In the process we relate several
different approaches formerly taken to deal with this problem, filling a gap
that appeared in a recent paper by Cibils. We also provide a counterexample to
a result concerning the Hochschild (co)homology appeared in a paper by J.A.
Guccione and J.J. Guccione.Comment: 11 pages, no figure
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