Exposition on affine and elliptic root systems and elliptic Lie algebras

2009/10/11 by Azam, Saeid, Yamane, Hiroyuki, Yousofzadeh, Malihe
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0910.1959

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.

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