Kyoto Journal of Mathematics

$3$-graded decompositions of exceptional Lie algebras $\mathfrak{g}$ and group realizations of $\mathfrak{g}_{ev}$, $\mathfrak{g}_{0}$ and $\mathfrak{g}_{ed}$, III: $G=E_{8}$

Abstract

In the articles [4] and [7], we completed the determination of group realizations $\mathfrak {g}_{ev}$ and $\mathfrak{g}_{0}$ of $2$-graded decompositions $\mathfrak {g}=\mathfrak {g}_{-2}\oplus \mathfrak {g}_{-1}\oplus \mathfrak {g}_{0}\oplus \mathfrak {g}_{1}\oplus \mathfrak {g}_{2}$ of exceptional Lie algebras $\mathfrak{g}$ for the universal exceptional Lie groups. In the present article, which is a continuation of [5] and [8], we determine group realizations of subalgebras $\mathfrak{g}_{ev}$, $\mathfrak{g}_{0}$ and $\mathfrak{g}_{ed}$ of $3$-graded decompositions of exceptional Lie algebras $\mathfrak{g}$ for the universal exceptional Lie groups of type $E_{8}$.

Article information

Source
Kyoto J. Math., Volume 50, Number 2 (2010), 281-305.

Dates
First available in Project Euclid: 7 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1273236817

Digital Object Identifier
doi:10.1215/0023608X-2009-014

Mathematical Reviews number (MathSciNet)
MR2666659

Zentralblatt MATH identifier
1221.17013

Subjects
Primary: 20G41: Exceptional groups

Citation

Miyashita, Toshikazu; Yokota, Ichiro. $3$ -graded decompositions of exceptional Lie algebras $\mathfrak{g}$ and group realizations of $\mathfrak{g}_{ev}$ , $\mathfrak{g}_{0}$ and $\mathfrak{g}_{ed}$ , III: $G=E_{8}$. Kyoto J. Math. 50 (2010), no. 2, 281--305. doi:10.1215/0023608X-2009-014. https://projecteuclid.org/euclid.kjm/1273236817

References

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