Month: December 2022

On coGalois Groups

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Canan Özeren, Dokuz Eylül University.
Date: 26th of December, 2022, Tuesday, Time: 13:30 – 15:30.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

Abstract:Torsion-free covers exist for abelian groups (see [1]).
The coGalois group of a torsion-free cover \phi: T \rightarrow A of an abelian group is defined in [2] as the group of f: T \rightarrow T s.t. \phi f= \phi and is denoted by G(\phi).
The abelian groups for which the coGalois group is trivial characterized in [3].
The notion of coGalois group can be defined in any category where we have a covering class.
In [4], coGalois groups are studied in the category of representation of quiver q_2 : \cdot \rightarrow \cdot .
We talk about the necessary conditions, give in [4], the coGalois group, associated to torsion free-cover, for an object in (q_2, Z-mod).

References

[1] E. Enochs: Torsion-free covering modules. (1963)

[2] E. Enochs, J. R. García Rozas and L. Oyonarte: Compact coGalois groups. (2000).

[3] E. Enochs and J. Rada: Abelian groups which have trivial absolute \ coGalois group. (2005).

[4] Paul Hill, Abelian group pairs having a trivial coGalois Group. (2006).

2022-2023 Fall Semester Make-up Exam Schedule

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Tuesday 20, December 202213.00MAT 2039 Differential Equations I
MAT 1015 Technical English I
MAT 3059 Numerical Analysis I		Place: Head of Department Office
Wednesday 21, December 202210.20MAT 1031 Calculus I
MAT 1035 Analytic Geometry
MAT 3055 Algebra I
MAT 4045 Galois Theory		Place: Head of Department Office
Wednesday 21, December 202213.00TDL 1001 Turkish Language IPlace: Head of Department Office

Coxeter Functors and Gabriel’s Theorem III

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İrem Yıldız, Dokuz Eylül University.
Date: 20th of December, 2022, Tuesday, Time: 13:30 – 15:30.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

Abstract: In this talk, we will introduce the basics of representation of quivers. We will define some functors which annihilate simples and carry indecomposables to indecomposables, which will help to prove Gabriel’s Theorem that states which types of quivers have finitely many isomorphisms classes of indecomposable representations.

References

[1] Some lecture notes in Bielefeld university from Henning Krause . 

[2] Article from I. N. Bernstein, I. M. Gel’fand, V. A. Ponomarev named “Coxeter functor and Gabriel ‘s theorem”.

Coxeter Functors and Gabriel’s Theorem II

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İrem Yıldız, Dokuz Eylül University.
Date: 13th of December, 2022, Tuesday, Time: 13:30 – 15:30.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

Abstract: In this talk, we will introduce the basics of representation of quivers. We will define some functors which annihilate simples and carry indecomposables to indecomposables, which will help to prove Gabriel’s Theorem that states which types of quivers have finitely many isomorphisms classes of indecomposable representations.

References

[1] Some lecture notes in Bielefeld university from Henning Krause . 

[2] Article from I. N. Bernstein, I. M. Gel’fand, V. A. Ponomarev named “Coxeter functor and Gabriel ‘s theorem”.

Coxeter Functors and Gabriel’s Theorem

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İrem Yıldız, Dokuz Eylül University.
Date: 6th of December, 2022, Tuesday, Time: 13:30 – 15:30.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

Abstract: In this talk, we will introduce the basics of representation of quivers. We will define some functors which annihilate simples and carry indecomposables to indecomposables, which will help to prove Gabriel’s Theorem that states which types of quivers have finitely many isomorphisms classes of indecomposable representations.

References

[1] Some lecture notes in Bielefeld university from Henning Krause . 

[2] Article from I. N. Bernstein, I. M. Gel’fand, V. A. Ponomarev named “Coxeter functor and Gabriel ‘s theorem”.