Exposition on affine and elliptic root systems and elliptic Lie algebras

2009/10/11 by Saeid Azam, Azam, Saeid, Hiroyuki Yamane +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.0910.1959

Submitted to RIMS Kokyuroku Bessatsu

arxiv created 2009/10/11 · openalex publication_date 2009/10/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Universal coverings of Lie tori (A finite presentation)

Related

• A characterization of minimal extended affine root systems (Relations to Elliptic Lie Algebras)
• A finite number of defining relations and a UCE theorem of the elliptic Lie algebras and superalgebras with rank ≥ 2
• Frobenius structures and characters of affine Lie algebras
• Classification of marked elliptic root systems with non-reduced affine quotient
• Classification of bases of twisted affine root supersystems