Lie polynomials in q-deformed algebras

MAM research frontier lecture series, PhD course, by Dr. Rafael Reno Cantuba,
Department of Mathematics and Statistics, De La Salle University, Manila,
organised by Mathematics and Applied Mathematics research environment MAM,
Division of Applied Mathematics, Mälardalen University, Västerås, Sweden.


 

Dr. Rafael Reno Cantuba , Department of Mathematics and Statistics, De La Salle University, Manila, Philippines is the recipient of the International Mathematical Union (IMU) 2018 Research Travel Grant hosted by Professor Sergei Silvestrov at the Research environment in Mathematics and Applied Mathematics MAM, Division of Applied Mathematics, Mälardalen University, Västerås, Sweden from September 1 to November 30. The International Mathematical Union IMU is an non-governmental and non-profit scientific organization. It aims to advance international cooperation in the field and support initiatives that contributes to the development of mathematical science.

Course content

This course of lectures aims to illustrate the application of abstract results from Algebra in actual computations and proofs about associative algebras that are important in current research and current literature concerned with associative algebras and their applications. Such results involve the Diamond Lemma for Ring Theory, and also the use of gradations and filtrations to simplify computations and proofs about associative algebras. The specific object of study is the universal Askey-Wilson algebra, as this provides a venue for the application of the said results and techniques at a reasonable level of computational difficulty for graduate students. Also, several important associative algebras are related to substructures of the universal Askey-Wilson algebra. These include the quantum groups Uq(sl2) and Uq(so3), the q-Onsager algebra, and also the q-deformed Heisenberg algebras. The goal for using these techniques is to distinguish the elements of the said algebras that are Lie polynomials in the generators from those which are not. Thus, there will also be a discussion of Lie polynomials, both in the general theory in which free algebras are the setting, and also in the specific cases of distinguishing Lie polynomials in the associative algebras mentioned. Each lecture shall be for approximately two hours. A description of the topics for each lecture is given in the following plan.

Plan of the lectures

Plan of the lectures can be downloaded here as pdf file (pdf 100 kB)

Time schedule and location:

October 24, Wednesday,16.15-17.00, U3-083 (Hilbert room), UKK, MDH, Västerås

October 31, Wednesday, 13.15-15.00, U3-083 (Hilbert room), UKK, MDH, Västerås

Cofee break

October 31, Wednesday, 15.30-16.45, U3-083 (Hilbert room), UKK, MDH, Västerås

November 6, Tuesday, 16.00-17.00, U3-083 (Hilbert room), UKK, MDH, Västerås

November 29, Thursday, 15.30-16.15, R2-605, MDH, Västerås

Contacts:

Dr. Rafael Cantuba

Professor Sergei Silvestrov