Incidence coalgebras of intervally finite posets, their integral quadratic forms and comodule categories

Representation of Quadratic Forms by Integral Quadratic Forms

Symmetry for Comodule Categories

For coalgebras C over a field, we study when the categories CM of left C-comodules and MC of right C-comodules are symmetric categories, in the sense that there is a duality between the categories of finitely presented unitary left R-modules and finitely presented unitary left L-modules, where R and L are the functor rings associated to the finitely accessible categories CM and MC .

Cyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras

In this paper we construct a cylindrical module A♮H for an Hcomodule algebra A, where the antipode of the Hopf algebra H is bijective. We show that the cyclic module associated to the diagonal of A♮H is isomorphic with the cyclic module of the crossed product algebra A ⋊H. This enables us to derive a spectral sequence for the cyclic homology of the crossed product algebra. We also construct a c...

Codes , Quadratic Forms and Finite

We study nonlinear binary error{correcting codes closely related to nite geometries and quadratic forms, and having links with ex-tremal Euclidean line{sets and with recently introducedcodes over Z 4. Our emphasis is on geometric and combinatorial properties of highly structured families of codes. The following diagram gives an indication of the main topics and inter-connections arising in this...

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.