I'm asked to prove that any two maximal torus in $SO(3)$ only intersects at the identity. This seems to be a work to find all maximal torus up to the conjugate class. I know that the subgroups $SO(2)$ which correspond to rotation around axis are maximal torus, and I doubt these are the all maximal torus, but I just can't find an argument to get justify this. Any hints on how to get start?
2026-04-09 00:22:35.1775694155
Maximal torus in $SO(3)$?
201 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GROUP-THEORY
- What is the intersection of the vertices of a face of a simplicial complex?
- Group with order $pq$ has subgroups of order $p$ and $q$
- How to construct a group whose "size" grows between polynomially and exponentially.
- Conjugacy class formula
- $G$ abelian when $Z(G)$ is a proper subset of $G$?
- A group of order 189 is not simple
- Minimal dimension needed for linearization of group action
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- subgroups that contain a normal subgroup is also normal
- Could anyone give an **example** that a problem that can be solved by creating a new group?
Related Questions in LIE-GROUPS
- Best book to study Lie group theory
- Holonomy bundle is a covering space
- homomorphism between unitary groups
- On uniparametric subgroups of a Lie group
- Is it true that if a Lie group act trivially on an open subset of a manifold the action of the group is trivial (on the whole manifold)?
- Find non-zero real numbers $a,b,c,d$ such that $a^2+c^2=b^2+d^2$ and $ab+cd=0$.
- $SU(2)$ adjoint and fundamental transformations
- A finite group G acts freely on a simply connected manifold M
- $SU(3)$ irreps decomposition in subgroup irreps
- Tensors transformations under $so(4)$
Related Questions in COMPACTNESS
- Every nonempty perfect set in $\mathbb R^k$ is uncountable: Rudin's argument
- Help in understanding proof of Heine-Borel Theorem from Simmons
- Is the distance between those compact sets equal to $0$?
- Are compact groups acting on Polish spaces essentially Polish?
- Set of Positive Sequences that Sum to 1 is Compact under Product Topology?
- The space $D(A^\infty)$
- Proving the one-point compactification of a topological space is a topology
- Never Used Compact Closure...
- Continuity of the maximal element of a multi-valued function
- Consider the metric space of infinite sequences of 0s and 1s under this metric.
Related Questions in ROTATIONS
- Properties of a eclipse on a rotated plane to see a perfect circle from the original plane view?
- why images are related by an affine transformation in following specific case?(background in computer vision required)
- Proving equations with respect to skew-symmetric matrix property
- Finding matrix linear transformation
- A property of orthogonal matrices
- Express 2D point coordinates in a rotated and translated CS
- explicit description of eigenvector of a rotation
- Finding the Euler angle/axis from a 2 axes rotation but that lies on the original 2 axes' plane
- How to find a rectangle's rotation amount that is inscribed inside an axis-aligned rectangle?
- Change of basis with rotation matrices
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?
Hints:
If $g \in \mathrm{SO}(3)$, what are its eigenvalues?
If $g, h \in \mathrm{SO}(3)$ commute, how does $g$ interact with the eigenspaces of $h$?