dorsal/arxiv
View Schema"Cayley-Klein" schemes for real Lie algebras and Freudhental Magic Squares
| Authors | Mariano Santander, Francisco J. Herranz |
|---|---|
| Categories | |
| ArXiv ID | physics/9702031 |
| URL | https://arxiv.org/abs/physics/9702031 |
| Journal | Group21. Physical Applications and Mathematical Aspects of Geometry, Groups and Algebras, Vol. I, Eds: H.D. Doebner, P. Nattermann, W. Scherer, (World Scientific, Singapore), 1997, pp.151-156 |
Abstract
We introduce three "Cayley-Klein" families of Lie algebras through realizations in terms of either real, complex or quaternionic matrices. Each family includes simple as well as some limiting quasi-simple real Lie algebras. Their relationships naturally lead to an infinite family of $3\times 3$ Freudenthal-like magic squares, which relate algebras in the three CK families. In the lowest dimensional cases suitable extensions involving octonions are possible, and for $N=1, 2$, the "classical" $3\times 3$ Freudenthal-like squares admit a $4\times 4$ extension, which gives the original Freudenthal square and the Sudbery square.
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"abstract": "We introduce three \"Cayley-Klein\" families of Lie algebras through\nrealizations in terms of either real, complex or quaternionic matrices. Each\nfamily includes simple as well as some limiting quasi-simple real Lie algebras.\nTheir relationships naturally lead to an infinite family of $3\\times 3$\nFreudenthal-like magic squares, which relate algebras in the three CK families.\nIn the lowest dimensional cases suitable extensions involving octonions are\npossible, and for $N=1, 2$, the \"classical\" $3\\times 3$ Freudenthal-like\nsquares admit a $4\\times 4$ extension, which gives the original Freudenthal\nsquare and the Sudbery square.",
"arxiv_id": "physics/9702031",
"authors": [
"Mariano Santander",
"Francisco J. Herranz"
],
"categories": [
"math-ph",
"math.MP"
],
"journal_ref": "Group21. Physical Applications and Mathematical Aspects of\n Geometry, Groups and Algebras, Vol. I, Eds: H.D. Doebner, P. Nattermann, W.\n Scherer, (World Scientific, Singapore), 1997, pp.151-156",
"title": "\"Cayley-Klein\" schemes for real Lie algebras and Freudhental Magic Squares",
"url": "https://arxiv.org/abs/physics/9702031"
},
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