The 33rd Lie Algebra Summer Seminar

 

Date: August 18 (Friday) and 19 (Saturday), 2017

Place : D509 (5th floor)  University of Tsukuba


August 18 (Friday)

14:00 -14:40  Automorphisms of locally affine root systems

                     Yoji Yoshii  Iwate University

14:40 - 15:20  On global and local triality for matrix algebras

                      Noriaki Kamiya  University of Aizu

15:20 - 15:40  Break

15:40 - 16:30  Conjugacy Theorem of the root bases of an affine root system

                      Hiroyuki Yamane  University of Toyama

16:40 - 17:30  Modules of twisted full toroidal Lie algebras

                      Punita Batra  Harish-Chandra Research Institute

18:30 - 20:30  Baquet

 

August 19 (Saturday)

 

10:00 - 10:40  Weyl group actions on the reflectable bases of a root system

                      Masaya Tomie   Morioka University

10:40 - 11:00  Break

11:00 - 11:50  On twisted Chevalley groups and Kac-Moody groups

                      Taiki Shibata   Okayama University of Science

11:50 - 12:00  Photo & Close the seminar

 

Abstract

Automorphisms of locally affine root systems,  YOSHII, Yoji

  We determine the automorphism group and Weyl group of a locally affine root system of type A.

 

On global and local triality for matrix algebras,  KAMIYA, Noriaki

  This talk is a generalization of derivations and automorphisms.

For matrix algebras, we will study them and also for the complex number and para Hurwitz algebras.

 

Modules of twisted full toroidal Lie algebras,  BATRA, Punita

  I will define full toroidal Lie algebras twisted by several finite order automorphisms and classify its integrable modules.

 

On twisted Chevalley groups and Kac-Moody groups,  SHIBATA, Taiki

  Untwisted/twisted affine Lie algebras are well understood and have a lot of applications

not only in mathematics but also in theoretical physics. On the other hand, infinite-dimensional ``Lie groups''

constructed from given affine Lie algebras (a la C. Chevalley), which we shall call affine Kac-Moody groups,

seem to be less understood. D. Peterson and V. Kac (1983) mentioned and Y. Chen (1996) proved that

an untwisted affine Kac-Moody group can be realized as a central extension of an algebraic loop group.

In this talk, we generalize the result to all twisted cases. Namely, we see that a similar central extension result

holds for all twisted affine Kac-Moody groups, by using the notions of twisted Chevalley groups

over a commutative ring (defined by E. Abe, 1976). This is a joint work with J. Morita (University of Tsukuba)

and A. Pianzola (University of Alberta).

 

Photo 1

 

Photo 2