SIGMA 22 (2026), 089, 19 pages      arXiv:2512.06340      https://doi.org/10.3842/SIGMA.2026.089

Subalgebras of the Universal Central Extension of $\mathfrak{sl}(n)[u^{\pm},v]$ from Two Involutions

Mamoru Ueda
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan

Received January 18, 2026, in final form August 31, 2026; Published online September 18, 2026

Abstract
The affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ is a deformation of the universal enveloping algebra of the universal central extension of $\mathfrak{sl}(n)[u^{\pm},v]$. In this article, we consider two involutions of the universal central extension of $\mathfrak{sl}(n)[u^{\pm},v]$ and give a presentation of the fixed subalgebras of these involutions. By deforming one fixed subalgebra, we can define the 1-parameter twisted affine Yangian $TY_{\hbar}(\widehat{\mathfrak{so}}(n))$, which is a coideal of the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$. Another fixed subalgebra is expected to define the 2-parameter twisted affine Yangian by deforming the presentation given in this article.

Key words: central extension; involution; twisted Yangian; twisted affine Yangian.

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