Research Output
Articles
Publication Date: 2025
Publications of the Research Institute for Mathematical Sciences (00345318)61(2)pp. 233-275
Extended affine root systems appear as the root systems of extended affine Lie algebras. A subclass of extended affine root systems, whose elements are called “minimal”, turns out to be of special interest, mostly because of the geometric properties of their Weyl groups; they possess the so-called presentation by conjugation. In this work, we characterize minimal extended affine root systems in terms of “minimal reflectable bases”, which resembles the concept of the “base” for finite and affine root systems. As an application, we construct elliptic Lie algebras by means of Serre-type generators and relations. © 2025 Research Institute for Mathematical Sciences, Kyoto University.
Publication Date: 2025
Journal of Algebra (00218693)680pp. 148-173
We investigate Chevalley bases for extended affine Lie algebras of type A1. The concept of integral structures for extended affine Lie algebras of rank greater than one has been successfully explored in recent years. However, for the rank one it has turned out that the situation becomes more delicate. In this work, we consider A1-type extended affine Lie algebras of nullity 2, known as elliptic extended affine Lie algebras. These Lie algebras are build using the Tits-Kantor-Koecher (TKK) construction by applying some specific Jordan algebras: the plus algebra of a quantum torus, the Hermitian Jordan algebra of the ring of Laurent polynomials equipped with an involution, and the Jordan algebra associated with a semilattice. By examining these ingredients we determine appropriate bases for null spaces of the corresponding elliptic extended affine Lie algebra leading to the establishment of Chevalley bases for these Lie algebras. © 2025 Elsevier Inc.
Publication Date: 2024
Journal of Algebraic Combinatorics (09259899)60(1)pp. 1-27
The behavior of objects associated with general extended affine Lie algebras is typically distinct from their counterparts in affine Lie algebras. Our research focuses on studying characters and Cartan automorphisms, which appear in the study of Chevalley involutions and Chevalley bases for extended affine Lie algebras. We show that for almost all extended affine Lie algebras, any finite-order Cartan automorphism is diagonal, and its corresponding combinatorial map is a character. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
Publication Date: 2023
Osaka Journal of Mathematics (00306126)60(3)pp. 613-635
Extended affine Lie superalgebras are super versions of extended affine Lie algebras and, more generally, invariant affine reflection algebras. By employing a method known as “affinization”, we construct several classes of extended affine Lie superalgebras of arbitrary nullity. © 2023, Osaka University. All rights reserved.
