Exposition on affine and elliptic root systems and elliptic Lie algebras
Saeid Azam, Hiroyuki Yamane, Malihe Yousofzadeh
TL;DR
This paper provides an explicit exposition on affine and elliptic root systems and elliptic Lie algebras, including proofs, definitions, and root multiplicities, enhancing understanding of their structure and properties.
Contribution
It offers a non-topological proof for affine root system bases, a Serre-type definition for elliptic Lie algebras, and details on isotropic root multiplicities.
Findings
Explicit non-topological proof for affine root system bases
Serre-type definition for elliptic Lie algebras with rank ≥ 2
Description of isotropic root multiplicities
Abstract
This is an exposition in order to give an explicit way to understand (1) a non-topological proof for an existence of a base of an affine root system, (2) a Serre-type definition of an elliptic Lie algebra with rank =>2, and (3) the isotropic root multiplicities of those elliptic Lie algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons