Number theory days

Session

Noncommutative algebra

25 juin 2014, 09:00

Salle de réunions (Université Lille 1)

Présidents de session

Noncommutative algebra

• Andre Leroy

10. Almost involutive Hopf algebras: are there additional symmetries in Hopf algebras besides the antipode?

Walter Ferrer-Santos (Universidad de la Republica, Montevideo)

25/06/2014 09:00

Noncommutative algebra

An involutory Hopf algebra is a Hopf algebra whose antipode squared equals the identity, $S^2=\operatorname{id}$. The identity map is an automorphism of Hopf algebras, hence it is tempting to substitute $\operatorname{id} \mapsto \sigma$ where $\sigma$ is an arbitray Hopf morphism and consider Hopf algebras whose antipode (that is an antimorphism of Hopf algebras) squared is the square of...

9. Some particular direct-sum decompositions and direct-product decompositions

Alberto Facchini (University of Padova)

25/06/2014 10:30

Noncommutative algebra

We will describe direct-sum decompositions and direct-product decompositions for some classes of modules. We will be mainly interested in direct sums and direct products of modules whose endomorphism rings have at most two maximal ideals.

14. Skew Generalized Quasi-Cyclic Codes

Patrick Solé (Telecom ParisTech)

25/06/2014 11:45

Noncommutative algebra

In this article we introduce skew generalized quasi-cyclic codes over finite field $F$ with Galois automorphism $\theta$. This is a generalization of quasi-cyclic codes and skew polynomial codes. These codes have an added advantage over quasi-cyclic codes, since the length of the code $C$ need not be a multiple of the index of $C$. After a brief description of the skew polynomial ring...