Volume 17, Issue Supplement 1, December 2010, Pages 103 - 161
The Classification of Almost Affine (Hyperbolic) Lie Superalgebras
Authors
Danil Chapovalov
iBusiness, Stockholm, Sweden,danil.chap@gmail.com
Maxim Chapovalov
Department of Mathematics, Stockholm University, Roslagsv. 101, Kräftriket hus 6, SE-106 91, Stockholm, Sweden
Alexei Lebedev
Nizhegorodskij Univ., pr. Gagarina 23, Nizhny Novgorod, RU-603950, Russia,yorool@mail.ru
Dimitry Leites
Department of Mathematics, Stockholm University, Roslagsv. 101, Kräftriket hus 6, SE-106 91, Stockholm, Sweden,mleites@math.su.se
Received 30 September 2008, Accepted 15 January 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925110000829How to use a DOI?
- Keywords
- Hyperbolic Lie superalgebra; almost affine Lie superalgebra
- Abstract
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.
- Copyright
- © 2010 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Danil Chapovalov AU - Maxim Chapovalov AU - Alexei Lebedev AU - Dimitry Leites PY - 2021 DA - 2021/01/07 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 - 10.1142/S1402925110000829 ID - Chapovalov2021 ER -