共查询到20条相似文献,搜索用时 328 毫秒
1.
In this paper, we study extensions between two finite irreducible conformal modules over the Schrödinger–Virasoro conformal algebra and the extended Schrödinger–Virasoro conformal algebra. Also, we classify all finite nontrivial irreducible conformal modules over the extended Schrödinger–Virasoro conformal algebra. As a byproduct, we obtain a classification of extensions of Heisenberg–Virasoro conformal modules. 相似文献
2.
Weiqiang Wang 《中国科学 数学(英文版)》2018,61(2):385-390
We conjecture an explicit bound on the prime characteristic of a field, under which theWeyl modules of affine sl2 and the minimal series modules of Virasoro algebra remain irreducible, and Goddard-Kent-Olive coset construction for affine sl2 is valid. 相似文献
3.
S. V. Kryukov 《Theoretical and Mathematical Physics》1998,114(3):266-275
We investigate the relation between the algebra
and the q-deformation of the Virasoro algebra. We calculate the BRST operator of the Drinfeld-Sokolov reduction and its cohomology.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 114, No. 3, pp. 337–348, March, 1998. 相似文献
4.
Weiqiang Wang 《中国科学 数学(英文版)》2018,(2)
We conjecture an explicit bound on the prime characteristic of a field, under which the Weyl modules of affine sl_2 and the minimal series modules of Virasoro algebra remain irreducible, and Goddard-Kent-Olive coset construction for affine sl_2 is valid. 相似文献
5.
本文具体计算了系数在超Schrödinger代数J(1/1)的平凡模和有限维不可约模中的第一阶上同调群与第二阶上同调群,并给出了系数在通用包络代数U(J(1/1))中J(1/1)的第一阶与第二阶上同调群的维数是无限维的. 相似文献
6.
Ran SHEN Yu Cai SU 《数学学报(英文版)》2007,23(1):189-192
We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenber-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module (and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series). 相似文献
7.
Let G be a rank n additive subgroup of C and Vir[G] the corresponding Virasoro algebra of rank n. In the present paper, irreducible weight modules with finite dimensional weight spaces over Vir[G] are completely determined. There are two different classes of them. One class consists of simple modules of intermediate series whose weight spaces are all 1-dimensional. The other is constructed by using intermediate series modules over a Virasoro subalgebra of rank n−1. The classification of such modules over the classical Virasoro algebra was obtained by O. Mathieu in 1992 using a completely different approach. 相似文献
8.
I. Ya. Aref’eva 《Proceedings of the Steklov Institute of Mathematics》2011,272(1):13-21
The paper presents recent achievements and open questions in string field theory that are related to the cohomology of BRST
operators. We sketch the construction of a nonpolynomial action based on cubic theory that uses the triviality of the BRST
operator in the so-called large algebra. We also construct special solutions of equations of motion in superstring field theory
and study the cohomology of a modified BRST operator near these solutions. 相似文献
9.
Xiao Ping Xu 《数学学报(英文版)》2015,31(2):177-200
By solving certain partial differential equations, we find the explicit decomposition of the polynomial algebra over the 56-dimensional basic irreducible module of the simple Lie algebra E7 into a sum of irreducible submodules. This essentially gives a partial differential equation proof of a combinatorial identity on the dimensions of certain irreducible modules of E7. We also determine two three-parameter families of irreducible submodules in the solution space of Cartan's well-known fourth-order E7-invariant partial differential equation. 相似文献
10.
Zhao Kaiming 《东北数学》1997,(2)
Representationsofq┐analogueoftheVirasoroAlgebra*)ZhaoKaiming(赵开明)(DepartmentofPureMath.,UniversityofWaterloo,Waterloo,Ontario... 相似文献
11.
We compute the cohomology of modules over the algebra of twisted chiral differential operators over the flag manifold. This is applied to (1) finding the character of G-integrable irreducible highest weight modules over the affine Lie algebra at the critical level, and (2) computing a certain elliptic genus of the flag manifold. The main tool is a result that interprets the Drinfeld–Sokolov reduction as a derived functor. 相似文献
12.
将sl2(R)上不可约Harish-Chandra模及sl2(R)上不可分解的Harish-Chandra模进行了完全分类,得到了与sl2(C)上模分类的不同形式.作为应用,又构造了实Virasoro代数的一类新的不可约表示. 相似文献
13.
《Journal of Algebra》2007,307(1):209-214
We show that the support of a simple weight module over the Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all non-trivial weight spaces of such module are infinite-dimensional. As a corollary we obtain that every simple weight module over the Virasoro algebra, having a non-trivial finite-dimensional weight space, is a Harish-Chandra module (and hence is either a simple highest or lowest weight module or a simple module from the intermediate series). This implies positive answers to two conjectures about simple pointed and simple mixed modules over the Virasoro algebra. 相似文献
14.
In this article,we compute cohomology groups of the semisimple Lie conformal algebra S =Vir × Cur g with coefficients in its irreducible modules for a finite-dimensional simple Lie algebra g. 相似文献
15.
We compute the space of Poisson traces on a classical W \mathcal{W} -algebra, i.e., linear functionals invariant under Hamiltonian derivations. Modulo any central character, this space identifies
with the top cohomology of the corresponding Springer fiber. As a consequence, we deduce that the zeroth Hochschild homology
of the corresponding quantum W \mathcal{W} -algebra modulo a central character identifies with the top cohomology of the corresponding Springer fiber. This implies that
the number of irreducible finite-dimensional representations of this algebra is bounded by the dimension of this top cohomology,
which was established earlier by C. Dodd using reduction to positive characteristic. Finally, we prove that the entire cohomology
of the Springer fiber identifies with the so-called Poisson-de Rham homology (defined previously by the authors) of the centrally
reduced classical W \mathcal{W} -algebra. 相似文献
16.
I. V. Mikityuk 《Ukrainian Mathematical Journal》1990,42(4):472-477
We investigate Verma modules V over the generalized Virasoro current algebrag, which is the semidirect sum of the Virasoro algebra and the central extension of a commutative algebra. It is shown that an arbitrary unitary representation with highest weight of algebrag is isomorphic to the tensor product of a unitary Fock representation ofg (or of a one-dimensional representation ofg) and a unitary representation with highest weight of the Virasoro algebra (considered as a representation of algebrag). This result is used to obtain formulas for the determinants of the matrices defining the Shapovalov form on Verma module V.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 532–538, April, 1990. 相似文献
17.
We explicitly compute the first and second cohomology groups of the Schrdinger algebra S(1) with coefficients in the trivial module and the finite-dimensional irreducible modules.We also show that the first and second cohomology groups of S(1) with coefficients in the universal enveloping algebras U(S(1))(under the adjoint action) are infinite dimensional. 相似文献
18.
Chunguang Xia 《代数通讯》2017,45(2):502-513
Motivated by a well-known theorem of Mathieu’s on Harish–Chandra modules over the Virasoro algebra and its super version, we show that an irreducible quasifinite module over two classes of Lie superalgebras 𝒮(q) of Block type is either a highest or lowest weight module or else a module of the intermediate series if q≠?1. For such a module over 𝒮(?1), we give a rough classification. 相似文献
19.
With the cohomology results on the Virasoro algebra, the authors
determine the second cohomology group on the twisted
Heisenberg-Virasoro algebra, which gives all deformations on the
twisted Heisenberg-Virasoro algebra. 相似文献
20.
Xu Xiang 《数学学报(英文版)》1997,13(2):161-168
In this paper we study the pointed representations of the Virasoro algebra. We show that unitary irreducible pointed representations
of the Virasoro algebra are Harish-Chandra representations, thus they either are of highest or lowest weights or have all
weight spaces of dimension 1. Further, we prove that unitary irreducible weight representations of Virasoro superalgebras
are either of highest weights or of lowest weights, hence they are also Harish-Chandra representations.
This work was supported by CNSF 相似文献