The Z₂ Orbifold of the Universal Affine Vertex Algebra

2018/04/22 by Masoumah Al-Ali, Al-Ali, Masoumah
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1804.08189

openalex publication_date 2018/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ≫ be a simple, finite-dimensional complex Lie algebra, and let V^k(≫) denote the universal affine vertex algebra associated to ≫ at level k. The Cartan involution on ≫ lifts to an involution on V^k(≫), and we denote by V^k(≫)^ℤ₂ the orbifold, or fixed-point subalgebra, under this involution. Our main result is an explicit minimal strong finite generating set for V^k(≫)^ℤ₂ for generic values of k. In the case ≫ = \gs\gl₂, we also determine the set of nongeneric values of k, where this set does not work.

Citations

• Local systems of vertex operators, vertex superalgebras and modules

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