Year: 2019
Type: article
Abstract: Let $\mathfrak {g}(A)$ be the Kac-Moody algebra with respect to a symmetrizable generalized Cartan matrix A. We give an explicit presentation of the fix-point Lie subalgebra $\mathfrak {k}(A)$ of $\mathfrak {g}(A)$ with respect to the Chevalley involution. It is a presentation of $\mathfrak {k}(A)$ involving inhomogeneous versions of the Serre relations, or, from a different perspective, a presentation generalizing the Dolan-Grady presentation of the Onsager algebra. In the finite and untwisted affine case we explicitly compute the structure constants of $\mathfrak {k}(A)$ in terms of a Chevalley type basis of $\mathfrak {k}(A)$ . For the symplectic Lie algebra and its untwisted affine extension we explicitly describe the one-dimensional representations of $\mathfrak {k}(A)$ .
Author: Jasper V. Stokman
Institution: University of Amsterdam
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,690
OpenAlex ID: W2897148602