68 research outputs found
On the dimension of the space of integrals on coalgebras
We study the injective envelopes of the simple right -comodules, and their
duals, where is a coalgebra. This is used to give a short proof and to
extend a result of Iovanov on the dimension of the space of integrals on
coalgebras. We show that if is right co-Frobenius, then the dimension of
the space of left -integrals on is for any left
-comodule of finite support, and the dimension of the space of right
-integrals on is for any right -comodule of
finite support. If is a coalgebra, it is discussed how far is the dual
algebra from being semiperfect. Some examples of integrals are computed
for incidence coalgebras
On Quillen's calculation of graded -theory
We adapt Quillen's calculation of graded K-groups of
Z-graded rings with support in N to graded
K-theory, allowing gradings in a product Z \times G with G an arbitrary
group. This in turn allows us to use inductions and calculate graded K-theory
of Z^m-graded rings. Here Z is the ring of integers and N positive natural
numbers
Braided Bialgebras of Type One
Braided bialgebras of type one in abelian braided monoidal categories are
characterized as braided graded bialgebras which are strongly
-graded both as an algebra and as a coalgebra
- …