Christian Edgar Lomp's Annual Report

Christian Edgar Lomp's Annual Report

Year: 

2017

Brief description of the research activities: 

Noetherian Affine Cellular
During my visit to Stuttgart in June/July I continued the investigation on Noetherian affine cellular algebras together with Steffen Koenig und Paula Carvalho. The research is not yet concluded and will be continued.

Simple Modules over quasi-local (commutative) rings
With Paula Carvalho and Patrick Smith, I finished a paper on the characterisation of commutative Non-Noetherian rings that satisfy a property that E.Matlis had shown for Noetherian commutative rings, namely that the injective hulls of simple modules is locally of finite length. The paper has been submitted to the special issue of IEJA dedicated the the late John Clark.

Ore extensions over weak Hopf algebras
With Alveri Sant'ana and our common PhD student Ricardo Leite dos Santos, we were able of extending a result of Panov from Hopf algebras to weak Hopf algebras. Panov's Theorem gives necessary and sufficient to extend a Hopf algebra structure on an algebra  to one of its Ore extensions. Thereby we were able of constructing more infinite dimensional weak Hopf algebras.

Apart from guiding two of my PhD students (Deividi Pansera and Ricardo Leite dos Santos) to a successful conclusion of their PhD thesis, I started new research topics with the following visitors:

  • Zara Nazemian: With Zara Nazemian I intended to characterise the structure of endomorphism rings of so-called isosimple modules, i.e. modules whose non-zero submdoules are isomorphic. (1.1. - 1.4.2017). This research topic was inconclusive, since Zara Nazemian left Porto.
  • Sonia Rueda: During a visit of Sonia Rueda (23.-28.1.2017) , we, Paula Carvalho and I, started working on differential resultants and centralizers of certain differential operator rings. This work will be continued in the future.
  • André Leroy: During a visit of André Leroy (23.-28.4.2017) we, Paula Carvalho and I started a project to understand Cojuhari’s D-structures as they seem to be a kind of "R-smash products". This research will be continued in the future.

 

Talks / Seminars / Courses : 

Seminars

Title:
“A brief introduction to cellular algebras via Temperley-Lieb algebras with an outlook to their affine versions"
Speakers
Christian Edgar Lomp
Date:
13.03.2017
Host institution:
Southwest Jiaotong University
Country:
China
Location / City:
Chengdu
Title:
“Ring theoretical properties of affine cellular algebras"
Speakers
Christian Edgar Lomp
Date:
13.03.2017
Host institution:
Southwest Jiaotong University
Country:
China
Location / City:
Chengdu
Title:
“Hopf algebras and Ore Extensions"
Speakers
Christian Edgar Lomp
Date:
29.03.2017
Host institution:
Universidade de Coimbra
Country:
Portugal
Location / City:
Coimbra
Title:
“Ring theoretical properties of affine cellular algebras."
Speakers
Christian Edgar Lomp
Date:
27.06.2017
Host institution:
Oberseminar IAZ, Universität Stuttgart
Country:
Germany
Location / City:
Stuttgart
Title:
“Ring theoretical properties of affine cellular algebras."
Speakers
Christian Edgar Lomp
Date:
25.07.2017
Host institution:
Graduiertenkolleg Experimentelle und konstruktive Algebra, RWTH Aachen
Country:
Germany
Location / City:
Aachen

Communications in international conferences

Title:
“Ring theoretical properties of affine cellular algebras."
Name of the event:
Noncommutative rings and their applications, V
Speakers
Christian Edgar Lomp
Talk:
Invited talk
Date:
12.06.2017 to 15.06.2017
Host institution:
Université d'Artois
Country:
France
Location / City:
Lens
Title:
Ring Theoretical Properties of Affine Cellular Algebras
Name of the event:
NONCOMMUTATIVE AND NON-ASSOCIATIVE ALGEBRAIC STRUCTURES IN PHYSICS AND GEOMETRY
Speakers
Christian Edgar Lomp
Talk:
Invited talk
Date:
30.08.2017 to 02.09.2017
Host institution:
Queen's University Belfast
Country:
UK
Location / City:
Belfast

Work visits: 

Universität Stuttgart
23. 06. 2017 - 23. 06. 2017

Southwest Jiaotong University (Chengdu, China)
09. - 18. 03. 2017