Journal of Nonlinear Mathematical Physics

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Volume 17, Issue Supplement 1, December 2010, Pages 253 - 309

Prolongs of (Ortho-)Orthogonal Lie (Super)Algebras in Characteristic 2

Authors
Uma N. Iyer
Department of Mathematics and Computer Science, Bronx Community College, Bronx, NY 10453, USA,uma.iyer@bcc.cuny.edu
Alexei Lebedev
Nizhegorodskij University, 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 25 October 2009, Available Online 7 January 2021.
DOI
10.1142/S1402925110000866How to use a DOI?
Keywords
Modular Lie algebra; modular Lie superalgebra
Abstract

Cartan described some of the finite dimensional simple Lie algebras and three of the four series of simple infinite dimensional vectorial Lie algebras with polynomial coefficients as prolongs, which now bear his name. The rest of the simple Lie algebras of these two types (finite dimensional and vectorial) are, if the depth of their grading is greater than 1, results of generalized Cartan–Tanaka–Shchepochkina (CTS) prolongs.

Here we are looking for new examples of simple finite dimensional modular Lie (super)algebras in characteristic 2 obtained as Cartan prolongs. We consider pairs (an (ortho-)orthogonal Lie (super)algebra or its derived algebra, its irreducible module) and compute the Cartan prolongs of such pairs. The derived algebras of these prolongs are simple Lie (super)algebras.

We point out several amazing phenomena in characteristic 2: a supersymmetry of representations of certain Lie algebras, latent or hidden over complex numbers, becomes manifest; the adjoint representation of some simple Lie superalgebras is not irreducible.

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
253 - 309
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925110000866How 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

risenwbib
TY  - JOUR
AU  - Uma N. Iyer
AU  - Alexei Lebedev
AU  - Dimitry Leites
PY  - 2021
DA  - 2021/01/07
TI  - Prolongs of (Ortho-)Orthogonal Lie (Super)Algebras in Characteristic 2
JO  - Journal of Nonlinear Mathematical Physics
SP  - 253
EP  - 309
VL  - 17
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925110000866
DO  - 10.1142/S1402925110000866
ID  - Iyer2021
ER  -