This note defines the abstract Jordan decomposition in an arbitrary Lie algebra. Abstract Jordan decomposition in a Lie algebra is unique when it exists iff its centre is zero. It seems that the abstract Jordan decomposition maybe not exist even when its centre is zero, who can show me an example?
2026-04-04 11:22:59.1775301779
Abstract Jordan decomposition maybe not exist
254 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 $so(4)$
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?