# Algebra

The research in the area of Algebra covers themes in the subareas of Algebraic Geometry, Number Theory, Theory of Representations of Algebras, Theory of Group Algebras and Theory of Codes.

Some problems addressed are: in Theory of Representations of Algebras, Hochschild cohomology, Igusa-Todorov function, derived category, Auslander-Reiten theory for triangular categories; in Group Algebra Theory, applications to error correction codes; in Algebraic Geometry Max Noether’s theorem for non-hyperelitic integral curves and singular rational curves: dimension and weight via semigroups of values are studied. In Number Theory, the focus is on Diophantine equations and zero-sum problems.

**Research Lines**

Lie algebra and its representations, Algebraic Geometry, Code Theory, Additive Number Theory, Algebraic Number Theory.

**Researchers**

Abílio Lemos Cardoso Júnior Calculation of invariants in weighted zero-sum problems and search for solutions to Diophantine equations involving Mersenne, Fibonacci and Lucas numbers. | |

Allan de Oliveira MouraBounds of poset codes and computation of invariant on zero-sum problems. | |

Anderson Tiago da SilvaError-correcting codes, calculation of invariants of linear codes, in particular, cyclic codes, codes on rings and codes on the Poset metric and the calculation of invariants in weighted zero-sum problems. | |

Lia Feital Fusaro AbrantesGeneralizations for Max Noether’s theorem for integral non-hyperelitic curves and estimating the dimension and weight of singular rational curves, via semigroups of values. | |

Marinês GuerreiroApplications of group algebras to error-correcting codes. Classification of representations of algebraic groups and Lie algebras. | |

Sônia FernandesHochschild cohomology, Igusa-Todorov functions, derived category, Auslander-Reiten theory for triangulated categories. |