The Classification of Almost Affine (Hyperbolic) Lie Superalgebras
- https://doi.org/10.1142/S1402925110000829How to use a DOI?
- Hyperbolic Lie superalgebra, almost affine Lie superalgebra
We say that an indecomposable Cartan matrix A with entries in the ground field is almost affine if the Lie (super)algebra determined by it is not finite dimensional or affine (Kac–Moody) but the Lie sub(super)algebra determined by any submatrix of A, obtained by striking out any row and any column intersecting on the main diagonal, is the sum of finite dimensional or affine Lie (super)algebras. A Lie (super)algebra with Cartan matrix is said to be almost affine if it is not finite dimensional or affine (Kac–Moody), and all of its Cartan matrices are almost affine.
We list all almost affine Lie superalgebras over complex numbers with indecomposable Cartan matrix correcting two earlier claims of classification.
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Cite this article
TY - JOUR AU - Danil Chapovalov AU - Maxim Chapovalov AU - Alexei Lebedev AU - Dimitry Leites PY - 2021 DA - 2021/01 TI - The Classification of Almost Affine (Hyperbolic) Lie Superalgebras JO - Journal of Nonlinear Mathematical Physics SP - 103 EP - 161 VL - 17 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110000829 DO - https://doi.org/10.1142/S1402925110000829 ID - Chapovalov2021 ER -