A geometric construction of U(\mathfrakn) for affine Kac-Moody algebras of type C_n

2023/03/11 by Alberto Castillo Gómez, Gómez, Alberto Castillo, Christof Geiß +1
Mathematics · Physics and Astronomy · #16G20 #17B20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2303.06260

openalex publication_date 2023/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by the work of Geiss, Leclerc and Schröer [Represent. Theory 20, (2016)] we realize the enveloping algebra of the positive part of an affine Kac-Moody Lie algebra of Dynkin type C_n as a generalized composition algebra of constructible functions on the varieties of locally free representations of the corresponding 1-Iwanaga-Gorenstein algebra H=H_ℂ(C,D,Ω) with minimal symmetrizer D and arbitrary orientation Ω. To this end, we exploit in several ways the fact that in this situation H is a string algebra.

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