Skip to main content
MathOverflow

Return to Question

replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
Source Link
Community Bot
Community Bot
  • 1
  • 2
  • 3

The Cartan subalgebras of a reductive Lie algebra are abelian.

Are there non-reductive Lie algebras with abelian Cartan subalgebras?

In fact, the elements of a Cartan subalgebra of a reductive Lie algebra are semisimple, so a weaker question is:

Are there non-reductive Lie algebras with abelian Cartan subalgebras all of whose elements are semisimple?

N.B.: I asked this earlier at math.SEmath.SE.

The Cartan subalgebras of a reductive Lie algebra are abelian.

Are there non-reductive Lie algebras with abelian Cartan subalgebras?

In fact, the elements of a Cartan subalgebra of a reductive Lie algebra are semisimple, so a weaker question is:

Are there non-reductive Lie algebras with abelian Cartan subalgebras all of whose elements are semisimple?

N.B.: I asked this earlier at math.SE.

The Cartan subalgebras of a reductive Lie algebra are abelian.

Are there non-reductive Lie algebras with abelian Cartan subalgebras?

In fact, the elements of a Cartan subalgebra of a reductive Lie algebra are semisimple, so a weaker question is:

Are there non-reductive Lie algebras with abelian Cartan subalgebras all of whose elements are semisimple?

N.B.: I asked this earlier at math.SE.

corrected spelling
Source Link
edit approved Jan 17, 2017 at 11:03
proofromthebook
edit approved Jan 17, 2017 at 11:03
proofromthebook
  • 115
  • 5

Lie algebras with abelian Cartan subalgebras.

The Cartan subalgebras of a reductive Lie algebra are abelian.

Are there non-reductive Lie algebras with abelian Cartan subalgebras?

In fact, the elements of a Cartan subalgebra of a reducitivereductive Lie algebra are semisimple, so a weaker question is:

Are there non-reductive Lie algberasalgebras with abelian Cartan subalgebras all of whose elements are semisimple?

N.B.: I asked this earlier at math.SE.

Lie algebras with abelian Cartan subalgebras.

The Cartan subalgebras of a reductive Lie algebra are abelian.

Are there non-reductive Lie algebras with abelian Cartan subalgebras?

In fact, the elements of a Cartan subalgebra of a reducitive Lie algebra are semisimple, so a weaker question is:

Are there non-reductive Lie algberas with abelian Cartan subalgebras all of whose elements are semisimple?

N.B.: I asked this earlier at math.SE.

Lie algebras with abelian Cartan subalgebras

The Cartan subalgebras of a reductive Lie algebra are abelian.

Are there non-reductive Lie algebras with abelian Cartan subalgebras?

In fact, the elements of a Cartan subalgebra of a reductive Lie algebra are semisimple, so a weaker question is:

Are there non-reductive Lie algebras with abelian Cartan subalgebras all of whose elements are semisimple?

N.B.: I asked this earlier at math.SE.

Source Link
Mariano Suárez-Álvarez
Mariano Suárez-Álvarez
  • 47.3k
  • 14
  • 147
  • 264

Lie algebras with abelian Cartan subalgebras.

The Cartan subalgebras of a reductive Lie algebra are abelian.

Are there non-reductive Lie algebras with abelian Cartan subalgebras?

In fact, the elements of a Cartan subalgebra of a reducitive Lie algebra are semisimple, so a weaker question is:

Are there non-reductive Lie algberas with abelian Cartan subalgebras all of whose elements are semisimple?

N.B.: I asked this earlier at math.SE.