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The compact exceptional Lie algebra \mathfrak g^c_2 as a twisted ring group.
- Source :
- Proceedings of the American Mathematical Society; Sep2024, Vol. 152 Issue 9, p3679-3688, 10p
- Publication Year :
- 2024
-
Abstract
- A new highly symmetrical model of the compact Lie algebra \mathfrak {g}^c_2 is provided as a twisted ring group for the group \mathbb {Z}_2^3 and the ring \mathbb {R}\oplus \mathbb {R}. The model is self-contained and can be used without previous knowledge on roots, derivations on octonions or cross products. In particular, it provides an orthogonal basis with integer structure constants, consisting entirely of semisimple elements, which is a generalization of the Pauli matrices in \mathfrak {su}(2) and of the Gell-Mann matrices in \mathfrak {su}(3). As a bonus, the split Lie algebra \mathfrak {g}_2 is also seen as a twisted ring group. [ABSTRACT FROM AUTHOR]
- Subjects :
- GROUP rings
PAULI matrices
CAYLEY numbers (Algebra)
INTEGERS
GENERALIZATION
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 152
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 178830303
- Full Text :
- https://doi.org/10.1090/proc/16821