<ruby id="d9npn"></ruby>

      <sub id="d9npn"><progress id="d9npn"></progress></sub>

      <nobr id="d9npn"></nobr>

      <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

      <th id="d9npn"><meter id="d9npn"></meter></th>

      Stack Exchange Network

      Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

      Visit Stack Exchange

      Questions tagged [lie-groups]

      Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

      4
      votes
      0answers
      153 views

      Gram-Schmidt map as a Riemannian submersion

      We equip $\mathrm{GL}(n,\mathbb{R})$ and $\mathrm{O}(n)$ with their left-invariant metrics, whose restrictions to the corresponding neutral elements is the standard inner product $\mathrm{Trace}(AB^{\...
      4
      votes
      3answers
      154 views

      Real points of reductive groups and connected components

      Let $\mathbf G$ be a connected reductive group over $\mathbb R$, and let $G = \mathbf G(\mathbb R)$. Then $G$ is not necessarily connected as a Lie group, e.g. $\mathbf G = \operatorname{GL}_n$. ...
      4
      votes
      1answer
      125 views

      An easier reference than “On the Functional Equations Satisfied by Eisenstein Series”?

      I'd like to learn about Eisenstein series so I started reading "On the Functional Equations Satisfied by Eisenstein Series"by Langlands. http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/pdf/...
      1
      vote
      0answers
      71 views

      Basic notation question involving Lie Groups and Lie algebras

      I just started reading "On the functional equations satisfied by Eisentstein series" by Langlands http://publications.ias.edu/sites/default/files/Eisenstein-ps.pdf . I wasn't sure of some notation/...
      2
      votes
      0answers
      23 views

      Compact image of adjoint action

      Let $G$ be a connected Lie group and $H$ a connected Lie-subgroup. Suppose that for every compact subset $K\subset G/H$ the $H$-orbit $H.K$ is relatively compact in $G/H$. Is it true that the image ...
      6
      votes
      3answers
      275 views

      $SO(m+1)$-equivariant maps from $S^m$ to $S^m$

      Let $G=SO(m+1)$ , $m \geq 2$, act in the standard way on $S^m$. Let $F:S^m \to S^m$ be a $G$-equivariant map, i.e., $g F(g^{-1}x) =F(x)$ for all $x \in S^m$ and $g \in G$. Question 1: Is F the ...
      2
      votes
      1answer
      102 views

      Simple modules for direct sum of simple Lie algebras

      I think that the following statement is true, but I do not know how to prove it. Let $\mathfrak{g}_1$ and $\mathfrak{g}_2$ be two real simple Lie algebras. If $M$ is a (infinite dimensional) complex ...
      1
      vote
      0answers
      63 views

      Homotopy classes of maps between special unitary Lie group. Correction [duplicate]

      An hour ago I asked a question (under the same title) but I used a wrong notation. Here is the improved version. We consider a special unitary Lie group $SU(n)$. Then its center is $\mathbb{Z}_n$ and ...
      5
      votes
      1answer
      197 views

      Homotopy classes of maps between special unitary Lie groups

      I am sorry to mislead the notations: $SU(n)$ should be replaced by $PSU(n)$. I will reformulate it now. We consider the special unitary Lie group $SU(n)$. Then its center is $\mathbb{Z}_n$ and we ...
      1
      vote
      1answer
      182 views

      Homotopy of group actions

      Let $G$ be a topological group and $X$ be a topological space. Let $\alpha$, $\beta:G\times X\to X$ be two group actions. We say that these two actions are homotopic actions if there is a continuous ...
      2
      votes
      0answers
      135 views

      More general form of Fourier inversion formula

      My question begins as follows: Suppose $G$ is a compact (Lie) group and $A$ is a $G$-module, and denote the action of $G$ on $A$ by $\alpha$. Fix $a\in A$ and view $$ f:g\mapsto \alpha_g(a) $$ as an $...
      5
      votes
      1answer
      154 views

      Definition of a Dirac operator

      So it seems that a Dirac operator acting on spinors on $\psi=\psi(\mathfrak{su}(2),\mathbb{C}^2)$ can be written in this case simply as: $D=\sum_{i,j} E_{ij}\otimes e_{ji}$, where $E_{ij}$ are ...
      3
      votes
      1answer
      87 views

      A converse of Cartan's automatic continuity theorem

      Let $G$ be a compact real Lie group. We say that $G$ has property $(*)$ if every abstract automorphism of $G$ is continuous. A theorem of Cartan says that if $G$ has perfect Lie algebra, it has ...
      2
      votes
      0answers
      108 views

      Milnor's conjecture on Lie group (co)homology and forgetful functor of extensions

      Let $G$ and $H$ be compact Lie groups, Consider $Ext_{Lie}(G,H)$ the set of isomorphism of extensions of Lie groups: $$ 1\rightarrow G\rightarrow M\rightarrow H\rightarrow 1 $$ There exists a ...
      3
      votes
      1answer
      202 views

      Extensions of compact Lie groups

      Let $G$, $H$ be two compact Lie groups (possibly disconnected). Two short exact sequences of compact Lie groups $$ 0\rightarrow G\rightarrow M_1 \rightarrow H\rightarrow 0, $$ $$ 0\rightarrow G\...

      15 30 50 per page
      特码生肖图
      <ruby id="d9npn"></ruby>

          <sub id="d9npn"><progress id="d9npn"></progress></sub>

          <nobr id="d9npn"></nobr>

          <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

          <th id="d9npn"><meter id="d9npn"></meter></th>

          <ruby id="d9npn"></ruby>

              <sub id="d9npn"><progress id="d9npn"></progress></sub>

              <nobr id="d9npn"></nobr>

              <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

              <th id="d9npn"><meter id="d9npn"></meter></th>