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Salvatore Siciliano
Salvatore Siciliano
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The simple Lie algebra $W(1,2)^{(2)}$ of dimension 3 over $GF(2)$ obviously contains 87 subspaces of dimension 1, but its automorphism group has order 6 (see e.g. section 5.3 of the paper "B. Eick: Some new simple Lie algebras in characteristic 2: J. Symbol. Comput. 45, 943 -- 951 (2010)"). It is then clear that this Lie algebra is not homogeneous.

The simple Lie algebra $W(1,2)^{(2)}$ of dimension 3 over $GF(2)$ obviously contains 8 subspaces of dimension 1, but its automorphism group has order 6 (see e.g. section 5.3 of the paper "B. Eick: Some new simple Lie algebras in characteristic 2: J. Symbol. Comput. 45, 943 -- 951 (2010)"). It is then clear that this Lie algebra is not homogeneous.

The simple Lie algebra $W(1,2)^{(2)}$ of dimension 3 over $GF(2)$ obviously contains 7 subspaces of dimension 1, but its automorphism group has order 6 (see e.g. section 5.3 of the paper "B. Eick: Some new simple Lie algebras in characteristic 2: J. Symbol. Comput. 45, 943 -- 951 (2010)"). It is then clear that this Lie algebra is not homogeneous.

Source Link
Salvatore Siciliano
Salvatore Siciliano
  • 5.9k
  • 26
  • 41

The simple Lie algebra $W(1,2)^{(2)}$ of dimension 3 over $GF(2)$ obviously contains 8 subspaces of dimension 1, but its automorphism group has order 6 (see e.g. section 5.3 of the paper "B. Eick: Some new simple Lie algebras in characteristic 2: J. Symbol. Comput. 45, 943 -- 951 (2010)"). It is then clear that this Lie algebra is not homogeneous.