TY - GEN
T1 - Pseudo-symmetric pairs for Kac-Moody algebras
AU - Regelskis, Vidas
AU - Vlaar, Bart
N1 - © 2022 American Mathematical Society. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/
PY - 2022/8/31
Y1 - 2022/8/31
N2 - Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces and real forms of complex Lie algebras, and are wellstudied in the context of symmetrizable Kac-Moody algebras. In this paper we study a generalization. Namely, we introduce the concept of a pseudoinvolution, an automorphism which is only required to act involutively on a stable Cartan subalgebra, and the concept of a pseudo-fixed-point subalgebra, a natural substitute for the fixed-point subalgebra. In the symmetrizable KacMoody setting, we give a comprehensive discussion of pseudo-involutions of the second kind, the associated pseudo-fixed-point subalgebras, restricted root systems and Weyl groups, in terms of generalizations of Satake diagrams.
AB - Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces and real forms of complex Lie algebras, and are wellstudied in the context of symmetrizable Kac-Moody algebras. In this paper we study a generalization. Namely, we introduce the concept of a pseudoinvolution, an automorphism which is only required to act involutively on a stable Cartan subalgebra, and the concept of a pseudo-fixed-point subalgebra, a natural substitute for the fixed-point subalgebra. In the symmetrizable KacMoody setting, we give a comprehensive discussion of pseudo-involutions of the second kind, the associated pseudo-fixed-point subalgebras, restricted root systems and Weyl groups, in terms of generalizations of Satake diagrams.
KW - automorphism group
KW - Kac-Moody algebras
KW - restricted Weyl group
KW - symmetric pairs
UR - http://www.scopus.com/inward/record.url?scp=85137998601&partnerID=8YFLogxK
UR - https://arxiv.org/abs/2108.00260
U2 - 10.1090/conm/780/15690
DO - 10.1090/conm/780/15690
M3 - Conference contribution
AN - SCOPUS:85137998601
SN - 978-1-4704-6520-9
VL - 780
T3 - Contemporary Mathematics
SP - 155
EP - 203
BT - Contemporary Mathematics. Virtual Conference Hypergeometry, Integrability and Lie Theory, 2020
A2 - Koelink, Erik
A2 - Kolb, Stefan
A2 - Reshetikhin, Nicolai
A2 - Vlaar, Bart
PB - American Mathematical Society
T2 - Virtual conference on Hypergeometry, Integrability and Lie Theory, 2020
Y2 - 7 December 2020 through 11 December 2020
ER -