<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

    <em id="zlul0"></em>

      <dl id="zlul0"></dl>
        <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
        <em id="zlul0"></em>

        <div id="zlul0"><ol id="zlul0"></ol></div>

        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-algebras]

        Lie algebras are algebraic structures which were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used. Related mathematical concepts include Lie groups and differentiable manifolds. See also the [Wiki page](http://en.wikipedia.org/wiki/Lie_algebra).

        2
        votes
        0answers
        44 views

        Finding function $g$ related to given harmonic $ f$ in a certain way

        I have a harmonic function $f$, so $\Delta(f)=0$. I need to find another scalar function $g$, such that: $\nabla(f)\cdot\nabla(g)=0$ (gradients orthogonal) $\nabla(f) \times \operatorname{Lie}(f,g)= ...
        -1
        votes
        1answer
        70 views

        Reference Request: Carnot Group Not Containing Group of Isometries

        This question is a follow-up to this post, from which I quote: Let $\mathfrak{e}$ be the 3-dimensional Lie algebra with basis $(H,X,Y)$ and bracket $[H,X]=Y$, $[H,Y]=-X$, $[X,Y]=0$. It is ...
        7
        votes
        1answer
        241 views

        Lie Algebra of Automorphism Group of $\mathbb{P}_k^1$

        Let $X$ be a scheme over an algebraically closed field $k$ and let $\operatorname{Aut}(X)$ denote the functor sending a $k$-scheme $T$ to the group $\operatorname{Aut}_T(X \times_k T)$ of ...
        4
        votes
        1answer
        69 views

        First adjoint cohomology space of simple Lie algebras

        Let $L$ be a central extension of a simple Lie algebra $\mathfrak{g}$ such that $L=[L,L]$. It is not difficult to see that if $H^1(\mathfrak{g}, \mathfrak{g})=0$ then $H^1(L,L)=0$. In other words, if ...
        3
        votes
        1answer
        63 views

        Distance between Verma modules in certain “strongly” standard filtrations

        On p. 128 of the book: Representations of Semisimple Lie Algebras in the BGG Category $\mathcal{O}$. I quote: "......Delorme arrives at vanishing criteria for Ext$^n(\mathcal{O})$ which are more ...
        2
        votes
        2answers
        72 views

        Symmetry of Casimirs of Lie algebras

        The dimensions of the invariant tensors (Casimirs) of the simple Lie algebras are known, but I nowhere could find whether they are completely symmetric or antisymmetric with respect to an variable ...
        4
        votes
        0answers
        73 views

        Panyushev's conjectured duality for root poset antichains

        In his 2004 paper "ad-nilpotent ideals of a Borel subalgebra: generators and duality" (https://www.sciencedirect.com/science/article/pii/S0021869303006380), Panyushev conjectured (Conjecture 6.1) the ...
        3
        votes
        2answers
        109 views

        Central extensions, contractions and deformations

        A Lie algebra $\mathfrak{g}$ has a central extension $\mathfrak{??}_{\mu}$ with central charge $\mu$. Is there a family of Lie algebras $\mathfrak{g}_{\alpha\mu}$, for which $\mathfrak{g}_{\alpha\mu} \...
        5
        votes
        2answers
        288 views

        For a fixed dominant weight $\lambda$, are almost all dominant weights in the same coset above it?

        First some notation as in e.g. the book by Humphreys on Lie Algebras. Let $E$ be an Euclidean space with inner product $(-,-)$, and denote $\langle v,w \rangle = \frac{2(v,w)}{(w,w)}$. Let $\Phi$ be ...
        1
        vote
        0answers
        41 views

        About reductive Levi subalgebra of a parabolic subalgebra

        According to Vinberg - Lie groups and invariant theory, given a real or complex algebraic Lie algebra $\mathfrak{h}$, its reductive subalgebra $\mathfrak{r}$ is called a reductive Levi subalgebra of $\...
        2
        votes
        1answer
        87 views

        About the setting of the book “Representations of Semisimple Lie Algebras in the BGG Category $\mathcal{O}$”

        I would like to ask about the setting of the book "Representations of Semisimple Lie Algebras in the BGG Category $\mathcal{O}$" by Humphreys. I would like to know whether the semisimple Lie algebra $\...
        0
        votes
        1answer
        56 views

        Weyl Group Element $w$ fixing a root, and its presentation as product of simple reflections $w=s_1\dots s_n$

        Let $\Phi$ be a root system and $\gamma \in \Phi$ a root. Let $W$ be the Weyl group and $\Delta$ a set of simple roots. Let $w \in W$ such that $w(\gamma)=\gamma$. Is it true that if $w=s_1\dots s_n$ ...
        5
        votes
        3answers
        368 views

        Existence of a weight of a representation in the fundamental Weyl chamber

        Let $\mathfrak g$ be a complex simple Lie algebra. Fix a Cartan subalgebra $\mathfrak h$ of $\mathfrak g$, let $\Delta$ denote the corresponding root system. Pick a partial order on $\mathfrak h$, ...
        4
        votes
        4answers
        295 views

        Homology of solvable (nilpotent) Lie algebras

        Let $\mathfrak{g}$ be a solvable Lie algebra over $\mathbb{C}$ and $\lambda\in(\mathfrak{g}/[\mathfrak{g},\mathfrak{g}])^*$ be a character of $\mathfrak{g}$. I'm interested in calculating homology for ...
        2
        votes
        0answers
        65 views

        Jordan decomposition of linear operators

        Let $V$ be a finite dimensional space over an algebraically closed field of characteristic $0$. Let $\mathfrak{g}$ be a Lie subalgebra of the general Lie algebra $gl(V)$. For any $\phi\in gl(V)$, let $...

        15 30 50 per page
        山西福彩快乐十分钟
          <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

          <em id="zlul0"></em>

            <dl id="zlul0"></dl>
              <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
              <em id="zlul0"></em>

              <div id="zlul0"><ol id="zlul0"></ol></div>
                <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

                <em id="zlul0"></em>

                  <dl id="zlul0"></dl>
                    <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
                    <em id="zlul0"></em>

                    <div id="zlul0"><ol id="zlul0"></ol></div>
                    北京赛车开奖结果 龙龙龙天衣有风 瓦伦西亚住宿 宝石探秘攻略 黄金公主克莱姆 恩波利地图 日日进财走势图 qq飞车手游s联赛 英超伯恩利vs加的夫城 十二生肖婚姻配对