Find an n dimensional space L of derivations, such that [l, l'] = 0 for l,l' in L. Any help or hints would be helpful
2026-03-26 18:40:59.1774550459
Space of derivations that give a Lie algebra
64 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ABSTRACT-ALGEBRA
- Feel lost in the scheme of the reducibility of polynomials over $\Bbb Z$ or $\Bbb Q$
- Integral Domain and Degree of Polynomials in $R[X]$
- Fixed points of automorphisms of $\mathbb{Q}(\zeta)$
- Group with order $pq$ has subgroups of order $p$ and $q$
- A commutative ring is prime if and only if it is a domain.
- Conjugacy class formula
- Find gcd and invertible elements of a ring.
- Extending a linear action to monomials of higher degree
- polynomial remainder theorem proof, is it legit?
- $(2,1+\sqrt{-5}) \not \cong \mathbb{Z}[\sqrt{-5}]$ as $\mathbb{Z}[\sqrt{-5}]$-module
Related 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 JACOBIAN
- Finding $Ax=b$ iteratively using residuum vectors
- When a certain subfield of $\mathbb{C}(x,y^2)$ is Galois
- Two variables with joint density: Change of variable technique using Jacobian for $U=\min(X,Y)$ and $V=\max(X,Y)$
- Jacobian determinant of a diffeomorphism on the unit shpere must equal $1$ or $-1$
- Physicists construct their potentials starting from the Laplace equation, why they do not use another differential operator, like theta Θ?
- Solution verification: show that the following functions are not differentiable
- Finding Jacobian of implicit function.
- Jacobian chain rule for function composition with rotation matrix
- Is there a way to avoid chain rules in finding this derivative of an integral?
- Computing the derivative of a matrix-vector dot product
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?
$\textbf{Fact}$: Let $G$ be a Lie group and $\mathfrak{g}$ it's Lie algebra. Then if $G$ is abelian, then so is $\mathfrak{g}$. Let $G = \mathbb{R}^n$.