A note on the conjugacy of Cartan subalgebras
1979 ◽
Vol 27
(2)
◽
pp. 163-166
Keyword(s):
AbstractThe conjugacy of Cartan subalgebras of a Lie algebra L over an algebraically closed field under the connected automorphism group G of L is inherited by those G-stable ideals B for which B/Ci is restrictable for some hypercenter Ci of B. Concequently, if L is a restrictable Lie algebra such that L/Ci restrictable for some hypercenter Ci of L, and if the Lie algebra of Aut L contains ad L, then the Cartan subalgebras of L are conjugate under G. (The techniques here apply in particular to Lie algebras of characteristic 0 and classical Lie algebras, showing how the conjugacy of Cartan subgroups of algebraic groups leads quickly in these cases to the conjugacy of Cartan subalgebras.)
1962 ◽
Vol 14
◽
pp. 293-303
◽
1976 ◽
Vol 79
(3)
◽
pp. 401-425
◽
Keyword(s):
2018 ◽
Vol 11
(05)
◽
pp. 1850063
Keyword(s):
2008 ◽
Vol 11
◽
pp. 280-297
◽
2017 ◽
Vol 147
(5)
◽
pp. 993-1008
◽
2021 ◽
Vol 12
(1)
◽
pp. 45-52
Keyword(s):
1965 ◽
Vol 25
◽
pp. 211-220
◽
2014 ◽
Vol 58
(1)
◽
pp. 169-181
◽