On the ‘strange formula’ of Freudenthal and de Vries. (English) Zbl 0699.17011
An elementary algebraic proof is given of Freudenthal’s Strange Formula dim \({\mathfrak g}=24 | \rho |^ 2\), where \({\mathfrak g}\) is a compact semisimple Lie algebra and \(\rho\) half the sum of a positive system of roots. The author uses the natural representation of \({\mathfrak g}\) in the spinor space of \({\mathfrak g}\) provided with the opposite of the Killing form.
Reviewer: H.de Vries
MSC:
| 17B20 | Simple, semisimple, reductive (super)algebras |
References:
| [1] | DOI: 10.2307/1970892 · Zbl 0249.22003 · doi:10.2307/1970892 |
| [2] | DOI: 10.2307/1997977 · Zbl 0402.22001 · doi:10.2307/1997977 |
| [3] | Freudenthal, Linear Lie Groups (1969) · Zbl 0377.22001 |
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