Discovering real lie subalgebras of e6 using Cartan decompositions Public Deposited

http://ir.library.oregonstate.edu/concern/defaults/jm214p65s

This is the publisher’s final pdf. The published article is copyrighted by AIP Publishing LLC and can be found at:  http://www.aip.org/.

Descriptions

Attribute NameValues
Alternative Title
  • Discovering real lie subalgebras of e[subscript 6] using Cartan decompositions
Creator
Abstract or Summary
  • The process of complexification is used to classify Lie algebras and identify their Cartan subalgebras. However, this method does not distinguish between real forms of a complex Lie algebra, which can differ in signature. In this paper, we show how Cartan decompositions of a complexified Lie algebra can be combined with information from the Killing form to identify real forms of a given Lie algebra. We apply this technique to sl(3, O), a real form of e(6) with signature (52, 26), thereby identifying chains of real subalgebras and their corresponding Cartan subalgebras within e(6). Motivated by an explicit construction of sl(3, O), we then construct an Abelian group of order 8 which acts on the real forms of e(6), leading to the identification of 8 particular copies of the 5 real forms of e(6), which can be distinguished by their relationship to the original copy of sl(3, O). C (C) 2013 AIP Publishing LLC.
Resource Type
Date Available
Date Issued
Citation
  • Wangberg, A., & Dray, T. (2013). Discovering real lie subalgebras of e(6) using cartan decompositions. Journal of Mathematical Physics, 54(8) doi:10.1063/1.4818503
Academic Affiliation
Series
Rights Statement
Funding Statement (additional comments about funding)
Publisher
Peer Reviewed
Language
Replaces
Additional Information
  • description.provenance : Made available in DSpace on 2013-09-30T15:24:44Z (GMT). No. of bitstreams: 1 DrayTevianMathematicsDiscoveringRealLie.pdf: 872854 bytes, checksum: fc07349f0d6f5db902da81044c401e11 (MD5) Previous issue date: 2013-08
  • description.provenance : Submitted by Deborah Campbell (deborah.campbell@oregonstate.edu) on 2013-09-30T15:21:45Z No. of bitstreams: 1 DrayTevianMathematicsDiscoveringRealLie.pdf: 872854 bytes, checksum: fc07349f0d6f5db902da81044c401e11 (MD5)
  • description.provenance : Approved for entry into archive by Deborah Campbell(deborah.campbell@oregonstate.edu) on 2013-09-30T15:24:43Z (GMT) No. of bitstreams: 1 DrayTevianMathematicsDiscoveringRealLie.pdf: 872854 bytes, checksum: fc07349f0d6f5db902da81044c401e11 (MD5)
ISBN
  • 10.1063/1.4818503

Relationships

In Administrative Set:
Last modified: 07/08/2017

Downloadable Content

Download PDF
Citations:

EndNote | Zotero | Mendeley

Items