Representations of Spin(4), Spin(2,2) and Spin(3,1)

In this essay we present an outer product on R^6, and we show that R^6 with this outer product can take three kinds of Lie brackets. We prove that R^6 with these Lie brackets take the structures of so(4), so(2,2) and so(3,1). We also deduce a 4-dimensional submanifold of R^6 with an almost complex s...

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Bibliographic Details
Published in:arXiv.org 2016-07
Main Authors: Delbaznasab, Ali, Molaei, MohammadReza
Format: Article
Language:English
Subjects:
Brackets
Manifolds (mathematics)
Online Access:Get full text
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Summary:In this essay we present an outer product on R^6, and we show that R^6 with this outer product can take three kinds of Lie brackets. We prove that R^6 with these Lie brackets take the structures of so(4), so(2,2) and so(3,1). We also deduce a 4-dimensional submanifold of R^6 with an almost complex structure.
ISSN:2331-8422