Paula Carvalho Lomp's Annual Report
Year:
2017
Brief description of the research activities:
During 2017 I kept on doing research in ring theory. The main topics of this year research were:
- Given a commutative Noetherian ring and a automorphism alpha, we addressed the question: when does the skew polynomial ring S=R[t; alpha] satisfies the property that for every simple S-module the injective hull of ES(V) has all its finitely generated submodules artinian. A complete characterisation is found when R is an affine algebra over a field K and alpha is a K-algebra automotphism; the property we are look at holds if and only if simple S-modules are finite dimensional over K. [Joint work with Ken Brown and Jerzy Matczuk. Results were submited for publication. Preprint available : arXiv:1705.06596]
- The same property as above was studied with a PhD student from UFRGS (Porto Alegre - Brasil) for diferential operator rings over commutative Noetherian rings for his PhD thesis under my co-supervision. [The work was finished and the Thesis defended in September 2017]
- Study of simple modules over commutative non-Noetherian semiprimary quasi-local rings. In case M is the maximal ideal and M^3=0, we obtain a description in terms of the dual space of the Socle of R. [Joint work with Christian Lomp and Patrick Smith. Results were submited for publication. Preprint available : arXiv:1711.10580]
- As a generalisation of Graham and Lehrer’s cellular algebras, affine cellular algebras have been introduced in [S. Koenig and C.C. Xi, Affine cellular algebras, Adv. Math. 229 (2012)] in order to treat affine versions of diagram algebras like affine Hecke algebras of type A and affine Temperley–Lieb algebras in a unifying fashion. Affine cellular algebras include Kleshchev’s graded quasihereditary algebras, Khovanov-Lauda-Rouquier algebras and various other classes of algebras. In this paper we will study ring theoretical properties of affine cellular algebras. The study of the Noetherian property for these agebras has been started. [Work in progress]
Talks / Seminars / Courses :
Seminars
Title:
On the representation Theory of some Noetherian Algebras
Date:
08.02.2017
Host institution:
Seminário do Programa de Doutoramento inter-universitário em matemática Coimbra-Porto
Country:
Portugal
Location / City:
Coimbra
Title:
Simple modules and their essential extensions for skew polynomial rings.
Date:
21.07.2017
Host institution:
Oberseminar, Institute for Algebra and Number theory, University of Stuttgart
Country:
Germany
Location / City:
Stuttgart
Title:
Ring theoretical properties of affine cellular algebras
Date:
11.05.2017
Host institution:
Seminarium Algebra, University of Warsaw
Country:
Poland
Location / City:
Warsaw
Communications in international conferences
Title:
Simple modules and their essential extensions for skew polynomial rings
Name of the event:
Non-commutative and nonassociative algebraic structures in geometry and physics
Talk:
Invited talk
Date:
30.08.2017 to 02.09.2017
Host institution:
Queen's University
Country:
UK
Location / City:
Belfast
Work visits:
- University of Warsaw to work with Jerzy Matczuck on the chain condition of some annihilators (May 7-15), partially supported by the Warsaw University.
- University of Stuttgart to work with Steffen Koenig on the Noetherianess condition of affine cellular algebras (July 22-31), partially supported by the University of Stuttgart.
Other information :
The following guests visited CMUP to work with me and Christian Lomp:
- Sonia Rueda, Universidad Politécnica de Madrid (23.-28.1.2017).
- Jerzy Matczuk, Warsaw University (1.-28.2.2017);
- André Leroy from Université d'Artois (23.-28.4.2017);