Journal of Nonlinear Mathematical Physics

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
https://doi.org/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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
17 - Supplement 1
Pages
103 - 161
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925110000829How to use a DOI?
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
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  -