I am looking for a proof, that the extension of a semisimple Lie algebra with a semisimple is again semisimple.
I know the Theorem of Weyl and the one of Levi, so I thought about maybe using them.
2026-03-28 16:44:16.1774716256
Extension of a semisimple Lie algebra with a semisimple Lie algebra is semisimple. Why?
224 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in LIE-ALGEBRAS
- Holonomy bundle is a covering space
- Computing the logarithm of an exponentiated matrix?
- Need help with notation. Is this lower dot an operation?
- On uniparametric subgroups of a Lie group
- Are there special advantages in this representation of sl2?
- $SU(2)$ adjoint and fundamental transformations
- Radical of Der(L) where L is a Lie Algebra
- $SU(3)$ irreps decomposition in subgroup irreps
- Given a representation $\phi: L \rightarrow \mathfrak {gl}(V)$ $\phi(L)$ in End $V$ leaves invariant precisely the same subspaces as $L$.
- Tensors transformations under $so(4)$
Related Questions in SEMISIMPLE-LIE-ALGEBRAS
- Why is a root system called a "root" system?
- Ideals of semisimple Lie algebras
- A theorem about semisimple Lie algebra
- A Lie algebra with trivial center and commutative radical
- Relation between semisimple Lie Algebras and Killing form
- If $\mathfrak{g}$ is a semisimple $\Rightarrow$ $\mathfrak{h} \subset \mathfrak{g} $ imply $\mathfrak{h} \cap \mathfrak{h}^\perp = \{0\}$
- How to tell the rank of a semisimple Lie algebra?
- If $H$ is a maximal toral subalgebra of $L$, then $H = H_1 \oplus ... \oplus H_t,$ where $H_i = L_i \cap H$.
- The opposite of Weyl's theorem on Lie algebras
- Show that the semisimple and nilpotent parts of $x \in L$ are the sums of the semisimple and nilpotent parts
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?