Christian Edgar Lomp's Annual Report
Year:
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
Communications in international conferences
Work visits:
Universität Stuttgart
23. 06. 2017 - 23. 06. 2017
Southwest Jiaotong University (Chengdu, China)
09. - 18. 03. 2017