All Questions
9 questions with no upvoted or accepted answers
8
votes
0
answers
1k
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Computational complexity of multiplication in a nilpotent group?
What is the computational complexity of multiplication in a Carnot group ?
Background: A Carnot group is a real nilpotent Lie group $N$ whose Lie algebra $Lie(N)$ admits a direct sum decomposition
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- 785
5
votes
0
answers
123
views
Conjugacy classes of plane k-jet group
Define $G(n, k)$ as a subgroup of $\rm{Aut}(\Bbb C[[x_1, \dots, x_n]]/\mathfrak m^{k+1})$ with identity linear part (so, group of $k$-jets of selfmaps of $\Bbb C^n$). I'm interested in the map from $G(...
- 4,600
3
votes
0
answers
98
views
Semisimple subgroup of Euclidean group
Let $G$ be a closed and connected semisimple subgroup of the Euclidean group $E(n)$ (the group of isometries of $\mathbb R^n$).
Can we prove that $G$ is conjugate to a subgroup of $O(n)$?
- 2,535
3
votes
0
answers
359
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Does Branching in the Weight Diagram affect an embedding?
All groups here are compact semisimple Lie groups. Out of laziness I will use $B_7$ to mean $Spin(15)$.
Suppose that one has a group $H$ and a subgroup $G$. The embedding determines the decomposition ...
- 5,191
2
votes
0
answers
199
views
Element conjugate to a maximal torus
It is well known that any element in a compact connected Lie group is conjugate to an element in a maximal torus. Let G be a Lie group that is not necessarily compact and/or connected. Let $x\in G$ ...
- 59
2
votes
0
answers
81
views
The centralizer and normalizer of products of (SU(n) $\times$ SU(p) $\times$ …) in U(m)
$\DeclareMathOperator\SU{SU}\DeclareMathOperator\U{U}\DeclareMathOperator\Spin{Spin}
$Consider the special unitary group $\SU(n)$ and the unitary group $\U(m)$.
Below I specify a specfic way to embed $...
- 10.5k
2
votes
0
answers
290
views
Automorphisms group of complex and real simple Lie algebras
$\DeclareMathOperator{\Inn}{\operatorname{Inn}}\DeclareMathOperator{\Aut}{\operatorname{Aut}}\DeclareMathOperator{\Out}{\operatorname{Out}}\DeclareMathOperator{\g}{\mathfrak{g}}$According to Wikipedia,...
- 2,147
1
vote
0
answers
201
views
Laplacian on two Lie groups have the same Lie algebra
I know that if $G$ is a Lie group and $\mathfrak g = span\{X_i, 1\leq i \leq n\}$ be its Lie algebra, where $\{X_i\}$ are the vector fields of $G$. Then, the Casimir-Laplacian of $G$ is given by
$$\...
- 650
1
vote
0
answers
189
views
Poincaré inequality for connected Lie groups
Let $G$ be a compactly generated second countable locally compact group, and let $\mu$ be a probability measure which is:
symmetric,
adapted (in the sense that there is no proper subgroup $H$ such ...
- 527