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Discovering real lie subalgebras of using Cartan decompositions
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10.1063/1.4818503
/content/aip/journal/jmp/54/8/10.1063/1.4818503
http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/8/10.1063/1.4818503

Figures

Image of FIG. 1.
FIG. 1.

Preferred subalgebra chains of .

Image of FIG. 2.
FIG. 2.

Four real forms of . An underline indicates the presence of , an overline indicates the presence of , each initial vertical line indicates the presence of one component of , and each final vertical line indicates the presence of one component of .

Image of FIG. 3.
FIG. 3.

Composition of associated Cartan maps of acting on real forms of , showing the maximal compact subalgebra under ϕ.

Image of FIG. 4.
FIG. 4.

The multiplication table under commutation for the subspaces of determined by the associated Cartan maps , , and . All elements square to .

Tables

Generic image for table
Table I.

Our preferred basis for

Generic image for table
Table II.

Intersections of subspaces , , , and .

Generic image for table
Table III.

Commutation structure of and .

Generic image for table
Table IV.

Compositions of associated Cartan maps and the corresponding subalgebras of .

Generic image for table
Table V.

Splitting of basis under .

Generic image for table
Table VI.

Splitting of basis under .

Generic image for table
Table VII.

Splitting of basis under .

Generic image for table
Table VIII.

Subalgebras of using Cartan decompositions.

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/content/aip/journal/jmp/54/8/10.1063/1.4818503
2013-08-23
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Discovering real lie subalgebras of e6 using Cartan decompositions
http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/8/10.1063/1.4818503
10.1063/1.4818503
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