The 33rd Lie Algebra Summer Seminar
Date: August 18 (Friday) and 19 (Saturday), 2017
Place : D509 (5th floor) University of Tsukuba
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).