lion8172
- 27
- 0
I read in Knapp's book on Lie algebras that "a 2-dimensional nilpotent Lie algebra is abelian." Why is this the case? Can somebody who knows please tell me?
Lie Algebra: Why is 2D Nilpotent Lie Algebra Abelian?
- Context: Graduate
- Thread starter lion8172
- Start date
-
- Tags
- Algebra Lie algebra
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
1 reply · 2K views
Discussion
Physics news on Phys.org
- 2,014
- 4
How many 2-dimensional Lie algebras are there (up to isomorphism)? There are two: one's abelian and the other's not. Try proving that the nonabliean one cannot be nilpotent.
Similar threads
Graduate How do we prove that a nonzero nilpotent Lie algebra has a nontrivial center?
- HDB1
- · Replies 9 ·
- Linear and Abstract Algebra
- Replies
- 9
Graduate What is the definition of quotient Lie algebra?
- HDB1
- · Replies 15 ·
- Linear and Abstract Algebra
- Replies
- 15
Undergrad The Lie algebra of ##\frak{so}(3)## without complexification
- redtree
- · Replies 2 ·
- Linear and Abstract Algebra
- Replies
- 2
Undergrad What Are Classical Lie Algebras A, B, C, and D?
- HDB1
- · Replies 4 ·
- Linear and Abstract Algebra
- Replies
- 4
Graduate About semidirect product of Lie algebra
- HDB1
- · Replies 19 ·
- Linear and Abstract Algebra
- Replies
- 19
Undergrad About derivations of lie algebra
- HDB1
- · Replies 5 ·
- Linear and Abstract Algebra
- Replies
- 5
Graduate About Schur's lemma in lie algebra
- HDB1
- · Replies 2 ·
- Linear and Abstract Algebra
- Replies
- 2
Graduate Questions about solvable Lie algebras
- HDB1
- · Replies 7 ·
- Linear and Abstract Algebra
- Replies
- 7
Graduate How to compute the Casimir element of Lie algebra sl(2)?
- HDB1
- · Replies 24 ·
- Linear and Abstract Algebra
- Replies
- 24
Undergrad What is the definition of a Semi-simple Lie algebra?
- Silviu
- · Replies 4 ·
- Linear and Abstract Algebra
- Replies
- 4