Cosets of affine vertex algebras inside larger structures

Creutzig T, Linshaw AR (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Journal of Algebra Elsevier

Book Volume: 517

Pages Range: 396-438

DOI: 10.1016/j.jalgebra.2018.10.007

Abstract

Given a finite-dimensional reductive Lie algebra g equipped with a nondegenerate, invariant, symmetric bilinear form B, let V^k(g,B) denote the universal affine vertex algebra associated to g and B at level k. Let A^k be a vertex (super)algebra admitting a homomorphism V^k(g,B)→A^k. Under some technical conditions on A^k, we characterize the coset Com(V^k(g,B),A^k) for generic values of k. We establish the strong finite generation of this coset in full generality in the following cases: A^k=V^k(g^′,B^′), A^k=V^k−l(g^′,B^′)⊗F, and A^k=V^k−l(g^′,B^′)⊗V^l(g^″,B^″). Here g^′ and g^″ are finite-dimensional Lie (super)algebras containing g, equipped with nondegenerate, invariant, (super)symmetric bilinear forms B^′ and B^″ which extend B, l∈C is fixed, and F is a free field algebra admitting a homomorphism V^l(g,B)→F. Our approach is essentially constructive and leads to minimal strong finite generating sets for many interesting examples. As an application, we give a new proof of the rationality of the simple N=2 superconformal algebra with c=[Formula presented] for all positive integers k.

Involved external institutions

University of Alberta

Canada (CA) University of Denver

United States (USA) (US)

How to cite

APA:

Creutzig, T., & Linshaw, A.R. (2019). Cosets of affine vertex algebras inside larger structures. Journal of Algebra, 517, 396-438. https://doi.org/10.1016/j.jalgebra.2018.10.007

MLA:

Creutzig, Thomas, and Andrew R. Linshaw. "Cosets of affine vertex algebras inside larger structures." Journal of Algebra 517 (2019): 396-438.

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