Pseudo-symmetric pairs for Kac-Moody algebras
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.
Item Type | Other |
---|---|
Uncontrolled Keywords | automorphism group; Kac-Moody algebras; restricted Weyl group; symmetric pairs |
Subjects | Mathematics(all) |
Date Deposited | 26 Jul 2024 11:20 |
Last Modified | 26 Jul 2024 11:20 |
-
picture_as_pdf - 2108.00260v3.pdf
Explore Further
Read more research from the creator(s):
Find work associated with the faculties and division(s):
- Department of Physics, Astronomy and Mathematics
- School of Physics, Engineering & Computer Science
- Mathematics and Theoretical Physics
Find other related resources: