共查询到20条相似文献,搜索用时 46 毫秒
1.
Hilja L. Huru 《Acta Appl Math》2008,101(1-3):121-132
We present a method for quantizing semisimple Lie algebras. In Huru (Russ. Math. [2007]) we defined quantizations of the braided Lie algebra structure on a finite dimensional graded vector space V by quantizations of braided derivations on the exterior algebra of V
*
. We find quantizations of semisimple Lie algebras in this setting using the grading by their roots and shall go through all
root systems, classical and exceptional.
相似文献
2.
J.W. Robbin 《Linear algebra and its applications》1975,10(2):95-102
Given a norm on a finite dimensional vector space V, we may consider the group of all linear automorphisms which preserve it. The Lie algebra of this group is a Lie subalgebra of the endomorphism algebra of V having two properties: (1) it is the Lie algebra of a compact subgroup, and (2) it is “saturated” in a sence made precise below. We show that any Lie subalgebra satisfying these conditions is the Lie algebra of the group of linear automorphisms preserving some norm. There is an appendix on elementary Lie group theory. 相似文献
3.
Curtis D. Bennett 《代数通讯》2013,41(9):4013-4036
In this article we give a new technique for exponentiating infinite dimensional graded representations of graded Lie algebras that allows for the exponentiation of some non-locally nilpotent elements. Our technique is to naturally extend the representation of the Lie algebra g on the space V naturally to a representation on a subspace £ of the dual space V *. After introducing the technique, we prove that it enables the exponentiation of all elements of free Lie Algebras and afhne Kac-Moody Lie algebras. 相似文献
4.
The aim of this work is to characterize the families of Frobenius (respectively, contact) solvable Lie algebras that satisfies the following condition: 𝔤 = 𝔥?V, where 𝔥?𝔤𝔩(V), |dim V?dim 𝔤|≤1 and NilRad(𝔤) = V, V being a finite dimensional vector space. In particular, it is proved that every complex Frobenius solvable Lie algebra is decomposable, whereas that in the real case there are only two indecomposable Frobenius solvable Lie algebras. 相似文献
5.
A.A. Baranov 《Archiv der Mathematik》1999,72(2):101-106
An algebra is called finitary if it consists of finite-rank transformations of a vector space. We classify finitary simple Lie algebras over an algebraically closed field of zero characteristic. It is shown that any such algebra is isomorphic to one of the following¶ (1) a special transvection algebra
\frak t(V,P)\frak t(V,\mit\Pi );¶ (2) a finitary orthogonal algebra
\frak fso (V,q)\frak {fso} (V,q); ¶ (3) a finitary symplectic algebra
\frak fsp (V,s)\frak {fsp} (V,s).¶Here V is an infinite dimensional K-space; q (respectively, s) is a symmetric (respectively, skew-symmetric) nondegenerate bilinear form on V; and P\Pi is a subspace of the dual V* whose annihilator in V is trivial: 0={v ? V | Pv=0}0=\{{v}\in V\mid \Pi {v}=0\}. 相似文献
6.
Jin Yun GUO Bing Jun LI Qiu Xian WU 《数学学报(英文版)》2006,22(3):849-854
In this paper, we prove that there is a natural equivalence between the category F1(x) of Koszul modules of complexity 1 with filtration of given cyclic modules as the factor modules of an exterior algebra A = ∧V of an m-dimensional vector space, and the category of the finite-dimensional locally nilpotent modules of the polynomial algebra of m - 1 variables. 相似文献
7.
Let K be an algebraically closed field of arbitrary characteristic and Γ an abelian multiplicative group equipped with a bicharacter ε: Γ × Γ → K*. It is proved that, for any finite-dimensional derivation simple color algebra A over K, there exists a simple color algebra S and a color vector space V such that A? S? Sε(V), where Sε(V) is the ε-symmetric algebra of V. As an application of this result, a necessary and sufficient condition such that a Lie color algebra is semisimple is obtained. 相似文献
8.
Dominique Manchon 《代数通讯》2013,41(5):1537-1551
For any field k of zero characteristic we give a functor from the category of k-vector spaces into the category of k-Hopf algebras, attaching to any vector space V its bitensorial pointed Hopf algebra Av. This Hopf algebra is graded, fulfills a universal property, and contains a remarkable subspace P of primitive elements, which as a conjecture may generate the Lie algebra Prim Av. In case V is finite-dimensional we exhibit a Hopf pairing between Avand Av-whose kernel contains the (Hopf) ideal generated by the elements of P of degree ? 2. 相似文献
9.
Let M : = Γ\G/K be the quotient of an irreducible Hermitian symmetric space G/K by a torsionfree cocompact lattice G ì G{\Gamma \subset G}. Let V be a complex irreducible representation of G. We give a Hodge decomposition of the cohomology of the Γ-module V in terms of the cohomologies of automorphic vector bundles on M associated to the Lie algebra cohomologies
H*(\mathfrak p+ ,V){H*({\mathfrak p}^{+} ,V)}. 相似文献
10.
Marte Rørvik Høyem 《Acta Appl Math》2010,109(1):61-73
We consider the Lie algebra that corresponds to the Lie pseudogroup of all conformal transformations on the plane. This conformal
Lie algebra is canonically represented as the Lie algebra of holomorphic vector fields in ℝ2≃ℂ. We describe all representations of
\mathfrakg\mathfrak{g}
via vector fields in J
0ℝ2=ℝ3(x,y,u), which project to the canonical representation, and find their algebra of scalar differential invariants. 相似文献
11.
Finite vs affine W-algebras 总被引:1,自引:0,他引:1
In Section 1 we review various equivalent definitions of a vertex algebra V. The main novelty here is the definition in terms of an indefinite integral of the λ-bracket. In Section 2 we construct,
in the most general framework, the Zhu algebra ZhuΓV, an associative algebra which “controls” Γ-twisted representations of the vertex algebra V with a given Hamiltonian operator H. An important special case of this construction is the H-twisted Zhu algebra ZhuH V. In Section 3 we review the theory of non-linear Lie conformal algebras (respectively non-linear Lie algebras). Their universal
enveloping vertex algebras (resp. universal enveloping algebras) form an important class of freely generated vertex algebras
(resp. PBW generated associative algebras). We also introduce the H-twisted Zhu non-linear Lie algebra ZhuH R of a non-linear Lie conformal algebra R and we show that its universal enveloping algebra is isomorphic to the H-twisted Zhu algebra of the universal enveloping vertex algebra of R. After a discussion of the necessary cohomological material in Section 4, we review in Section 5 the construction and basic
properties of affine and finite W-algebras, obtained by the method of quantum Hamiltonian reduction. Those are some of the
most intensively studied examples of freely generated vertex algebras and PBW generated associative algebras. Applying the
machinery developed in Sections 3 and 4, we then show that the H-twisted Zhu algebra of an affine W-algebra is isomorphic to the finite W-algebra, attached to the same data. In Section 6
we define the Zhu algebra of a Poisson vertex algebra, and we discuss quasiclassical limits. In the Appendix, the equivalence
of three definitions of a finite W-algebra is established.
“I am an old man, and I know that a definition cannot be so complicated.” I.M. Gelfand (after a talk on vertex algebras in
his Rutgers seminar) 相似文献
12.
We analyse here a semilinear stochastic partial differential equation of parabolic type where the diffusion vector fields
are depending on both the unknown function and its gradient ∂
xu with respect to the state variable, ∈ ℝn. A local solution is constructed by reducing the original equation to a nonlinear parabolic one without stochastic perturbations
and it is based on a finite dimensional Lie algebra generated by the given diffusion vector fields. 相似文献
13.
If K is a Lie group and q : P → M is a principal K-bundle over the compact manifold M, then any invariant symmetric V-valued bilinear form on the Lie algebra
\mathfrakk{\mathfrak{k}} of K defines a Lie algebra extension of the gauge algebra by a space of bundle-valued 1-forms modulo exact 1-forms. In this article,
we analyze the integrability of this extension to a Lie group extension for non-connected, possibly infinite-dimensional Lie
groups K. If K has finitely many connected components, we give a complete characterization of the integrable extensions. Our results on
gauge groups are obtained by the specialization of more general results on extensions of Lie groups of smooth sections of
Lie group bundles. In this more general context, we provide sufficient conditions for integrability in terms of data related
only to the group K. 相似文献
14.
Rachelle C. DeCoste 《manuscripta mathematica》2008,127(3):309-343
We study the distribution of closed geodesics on nilmanifolds Γ \ N arising from a 2-step nilpotent Lie algebra constructed from an irreducible representation of a compact semisimple Lie algebra on a real finite dimensional vector space U. We determine sufficient conditions on the semisimple Lie algebra for Γ \ N to have the density of closed geodesics property where Γ is a lattice arising from a Chevalley rational structure on . 相似文献
15.
We consider the flow of a stochastic differential equation on d-dimensional Euclidean space. We show that if the Lie algebra generated by its diffusion vector fields is finite dimensional
and solvable, then the flow is conjugate to the flow of a non-autonomous random differential equation, i.e. one can be transformed
into the other via a random diffeomorphism of d-dimensional Euclidean space. Viewing a stochastic differential equation in this form which appears closer to the setting
of ergodic theory, can be an advantage when dealing with asymptotic properties of the system. To illustrate this, we give
sufficient criteria for the existence of global random attractors in terms of the random differential equation, which are
applied in the case of the Duffing-van der Pol oscillator with two independent sources of noise.
Received: 25 May 1999 / Revised version: 19 October 2000 / Published online: 26 April 2001 相似文献
16.
Mihalis Maliakas 《代数通讯》2013,41(6):2054-2062
Let V be an even dimensional vector space over a field K of characteristic 2 equipped with a nondegenerate alternating bilinear form f. The divided power algebra DV is considered as a complex with differential defined from f. We examine the cohomology modules as representations of the corresponding symplectic group. 相似文献
17.
Michael Klotz 《Geometriae Dedicata》2011,154(1):161-182
A {1}-structure on a Banach manifold M (with model space E) is an E-valued 1-form on M that induces on each tangent space an isomorphism onto E. Given a Banach principal bundle P with connected base space and a {1}-structure on P, we show that its automorphism group can be turned into a Banach–Lie group acting smoothly on P provided the Lie algebra of infinitesimal automorphisms consists of complete vector fields. As a consequence we show that
the automorphism group of a connected geodesically complete affine Banach manifold M can be turned into a Banach–Lie group acting smoothly on M. 相似文献
18.
C. Molitor-Braun 《manuscripta mathematica》1998,96(1):23-35
Let V be an exponential ?-module, ? being an exponential Lie algebra. Put ? = exp ?. Then every orbit of V under the action of ? admits a closed orbit in its closure. If G= exp ? is a nilpotent Lie group and ? an exponential algebra of derivations of ?, then ? = exp ? acts on G, L
1(G), (?) and the maximal ?-invariant ideals of L
1(G), resp. of (?) coincide with the kernels Ker Ω, resp. Ker Ω∩ (?), where Ω is a closed orbit of ?*.
Received: 6 December 1996 / Revised version: 7 December 1997 相似文献
19.
Given an algebraically closed field F of characteristic 0 and an F-vector space V, let L(V)?=?V⊕Λ2(V) denote the free 2-step nilpotent Lie algebra associated to V. In this paper, we classify all uniserial representations of the solvable Lie algebra 𝔤?=??x??L(V), where x acts on V via an arbitrary invertible Jordan block. 相似文献
20.
The Lie module of the group algebra
F\mathfrakSn{{F\mathfrak{S}_n}} of the symmetric group is known to be not projective if and only if the characteristic p of F divides n. We show that in this case its non-projective summands belong to the principal block of
F\mathfrakSn{{F\mathfrak{S}_n}} . Let V be a vector space of dimension m over F, and let L
n
(V) be the n-th homogeneous part of the free Lie algebra on V; this is a polynomial representation of GL
m
(F) of degree n, or equivalently, a module of the Schur algebra S(m, n). Our result implies that, when m ≥ n, every summand of L
n
(V) which is not a tilting module belongs to the principal block of S(m, n), by which we mean the block containing the n-th symmetric power of V. 相似文献