Adjoint dimension of a direct Lie algebra sum/product [on hold]
Let $L_1,L_2$ be Lie algebras (not necessarily semisimple), $d_1,d_2$ the dimensions of the defining irrep and $D_1,D_2$ the dimension of the adjoint irrep. Let $L_3=L_1bigoplus L_2$ and $L_4=L_1bigotimes L_2$ and $d_3,d_4,D_3,D_4$ the respective dimensions of their defining and adjoint irrep. Can you express them in $d_1,d_2,D_1,D_2$? (Yes, the question is semisimple :-)
lie-algebras
asked 2 days ago
Hauke ReddmannHauke Reddmann
1873
put on hold as off-topic by Dietrich Burde, amWhy, Jyrki Lahtonen, Paul Frost, Shailesh 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Dietrich Burde, amWhy, Paul Frost, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
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Let $L_1,L_2$ be Lie algebras (not necessarily semisimple), $d_1,d_2$ the dimensions of the defining irrep and $D_1,D_2$ the dimension of the adjoint irrep. Let $L_3=L_1bigoplus L_2$ and $L_4=L_1bigotimes L_2$ and $d_3,d_4,D_3,D_4$ the respective dimensions of their defining and adjoint irrep. Can you express them in $d_1,d_2,D_1,D_2$? (Yes, the question is semisimple :-)
lie-algebras
asked 2 days ago
Hauke ReddmannHauke Reddmann
1873
put on hold as off-topic by Dietrich Burde, amWhy, Jyrki Lahtonen, Paul Frost, Shailesh 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Dietrich Burde, amWhy, Paul Frost, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
2
Would you mind adding a bit of context, describe the exact situation etc. ... As it is now, I for my part just don't understand the question.
– Torsten Schoeneberg
2 days ago
add a comment |
Let $L_1,L_2$ be Lie algebras (not necessarily semisimple), $d_1,d_2$ the dimensions of the defining irrep and $D_1,D_2$ the dimension of the adjoint irrep. Let $L_3=L_1bigoplus L_2$ and $L_4=L_1bigotimes L_2$ and $d_3,d_4,D_3,D_4$ the respective dimensions of their defining and adjoint irrep. Can you express them in $d_1,d_2,D_1,D_2$? (Yes, the question is semisimple :-)
lie-algebras
asked 2 days ago
Hauke ReddmannHauke Reddmann
1873
Let $L_1,L_2$ be Lie algebras (not necessarily semisimple), $d_1,d_2$ the dimensions of the defining irrep and $D_1,D_2$ the dimension of the adjoint irrep. Let $L_3=L_1bigoplus L_2$ and $L_4=L_1bigotimes L_2$ and $d_3,d_4,D_3,D_4$ the respective dimensions of their defining and adjoint irrep. Can you express them in $d_1,d_2,D_1,D_2$? (Yes, the question is semisimple :-)
lie-algebras
lie-algebras
asked 2 days ago
Hauke ReddmannHauke Reddmann
1873
asked 2 days ago
Hauke ReddmannHauke Reddmann
1873
edited yesterday
Hauke Reddmann
asked 2 days ago
Hauke ReddmannHauke Reddmann
1873
asked 2 days ago
Hauke ReddmannHauke Reddmann
1873
asked 2 days ago
Hauke ReddmannHauke Reddmann
1873
1873
put on hold as off-topic by Dietrich Burde, amWhy, Jyrki Lahtonen, Paul Frost, Shailesh 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Dietrich Burde, amWhy, Paul Frost, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Dietrich Burde, amWhy, Jyrki Lahtonen, Paul Frost, Shailesh 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Dietrich Burde, amWhy, Paul Frost, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
2
Would you mind adding a bit of context, describe the exact situation etc. ... As it is now, I for my part just don't understand the question.
– Torsten Schoeneberg
2 days ago
add a comment |
2
Would you mind adding a bit of context, describe the exact situation etc. ... As it is now, I for my part just don't understand the question.
– Torsten Schoeneberg
2 days ago
2
2
Would you mind adding a bit of context, describe the exact situation etc. ... As it is now, I for my part just don't understand the question.
– Torsten Schoeneberg
2 days ago
Would you mind adding a bit of context, describe the exact situation etc. ... As it is now, I for my part just don't understand the question.
– Torsten Schoeneberg
2 days ago
add a comment |
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Would you mind adding a bit of context, describe the exact situation etc. ... As it is now, I for my part just don't understand the question.
– Torsten Schoeneberg
2 days ago