A. Castillo-Ramirez
Idempotents of the Norton-Sakuma algebras
Castillo-Ramirez, A.
Authors
Abstract
The concept of Majorana representation was introduced by A. A. Ivanov (2009), as a tool to identify and study subalgebras of the Conway–Griess–Norton Monster algebra . Sakuma's theorem in “6-transposition property of -involutions of vertex operator algebras”, Int. Math. Res. Not. IMRN 2007 (2007), Article ID rnm030, states that there are eight possibilities for the isomorphism type of an algebra with scalar product generated by a pair of distinct Majorana axes. These algebras, now known as the Norton–Sakuma algebras, were described by S. P. Norton (1982) as 2-generated subalgebras of and labelled by types , , , , , , and . In the present paper, we contribute to the understanding of the Norton–Sakuma algebras by finding all their idempotent elements and their automorphism groups. In particular, we find that an algebra of type has infinitely many idempotents of length 2, and that an algebra of type has exactly 208 idempotents.
Citation
Castillo-Ramirez, A. (2013). Idempotents of the Norton-Sakuma algebras. Journal of Group Theory, 16(3), 419-444. https://doi.org/10.1515/jgt-2012-0048
Journal Article Type | Article |
---|---|
Publication Date | May 2, 2013 |
Deposit Date | Feb 19, 2015 |
Journal | Journal of Group Theory |
Print ISSN | 1433-5883 |
Electronic ISSN | 1435-4446 |
Publisher | De Gruyter |
Peer Reviewed | Peer Reviewed |
Volume | 16 |
Issue | 3 |
Pages | 419-444 |
DOI | https://doi.org/10.1515/jgt-2012-0048 |
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search