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 | Book Section |
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Additional information | © 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/ |
Keywords | automorphism group, kac-moody algebras, restricted weyl group, symmetric pairs, general mathematics |
Date Deposited | 15 May 2025 16:48 |
Last Modified | 30 May 2025 23:19 |