Zobrazeno 1 - 10
of 23
pro vyhledávání: '"Genqiang Liu"'
Publikováno v:
Journal of Algebra. 575:1-13
In this paper, we study weight representations over the Schrodinger Lie algebra s n for any positive integer n. It turns out that the algebra s n can be realized by polynomial differential operators. Using this realization, we give a complete classif
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7f92c3496a532b400a91465d47cb8bf1
https://doi.org/10.1016/j.jalgebra.2021.01.034
https://doi.org/10.1016/j.jalgebra.2021.01.034
Autor:
Genqiang Liu, Kaiming Zhao
Publikováno v:
Transformation Groups. 27:1025-1044
The rank n symplectic oscillator Lie algebra 𝔤n is the semidirect product of the symplectic Lie algebra 𝔰𝔭2n and the Heisenberg algebra Hn. In this paper, we first study weight modules with finite-dimensional weight spaces over 𝔤n. When t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7931fecf25580c83d63bb80131ec83db
https://doi.org/10.1007/s00031-021-09639-y
https://doi.org/10.1007/s00031-021-09639-y
Autor:
Mengnan Niu, Genqiang Liu
Publikováno v:
Communications in Algebra. 49:2091-2100
For a commutative algebra A over C, denote g=Der(A). A module over the smash product A#U(g) is called a jet g-module, where U(g) is the universal enveloping algebra of g. In the present paper, we s...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::64ee22166efba67e7862a5f21fc27f94
https://doi.org/10.1080/00927872.2020.1862857
https://doi.org/10.1080/00927872.2020.1862857
Autor:
Yang Li, Genqiang Liu
Publikováno v:
Glasgow Mathematical Journal. 63:266-279
In this paper, we study the BGG category $\mathcal{O}$ for the quantum Schr{\"o}dinger algebra $U_q(\mathfrak{s})$, where $q$ is a nonzero complex number which is not a root of unity. If the central charge $\dot z\neq 0$, using the module $B_{\dot z}
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3d63fd631f40d6153202178d1a7be529
https://doi.org/10.1017/s0017089520000166
https://doi.org/10.1017/s0017089520000166
Publikováno v:
Moscow Mathematical Journal. 20:43-65
Let $d\ge1$ be an integer, $W_d$ and $\mathcal{K}_d$ be the Witt algebra and the weyl algebra over the Laurent polynomial algebra $A_d=\mathbb{C} [x_1^{\pm1}, x_2^{\pm1}, ..., x_d^{\pm1}]$, respectively. For any $\mathfrak{gl}_d$-module $M$ and any a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e2a0aeda79ae3951262c0512729b8ff4
https://doi.org/10.17323/1609-4514-2020-20-1-43-65
https://doi.org/10.17323/1609-4514-2020-20-1-43-65
Publikováno v:
Arkiv foer Matematik; 2023, Vol. 61 Issue 1, p123-140, 18p
Publikováno v:
Journal of Algebra. 511:164-181
For an irreducible module P over the Weyl algebra K n + (resp. K n ) and an irreducible module M over the general linear Lie algebra gl n , using Shen's monomorphism, we make P ⊗ M into a module over the Witt algebra W n + (resp. over W n ). We obt
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::83ca02ceeca2d4209f0369ac29cbaa99
https://doi.org/10.1016/j.jalgebra.2018.06.021
https://doi.org/10.1016/j.jalgebra.2018.06.021
Publikováno v:
Journal of Geometry and Physics. 129:208-216
In 2006, Gao and Zeng (Gao and Zeng, 2006) gave the free field realizations of highest weight modules over the extended affine Lie algebras g l 2 ( C q ) for any nonzero q ∈ C . In the present paper, applying the technique of localization to those
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ad8395de589568fd9909461646a79a44
https://doi.org/10.1016/j.geomphys.2018.03.003
https://doi.org/10.1016/j.geomphys.2018.03.003
Publikováno v:
Journal of Algebra. 502:146-162
A class of generalized Verma modules over sl n + 2 are constructed from sl n + 1 -modules which are U ( h n ) -free modules of rank 1. The necessary and sufficient conditions for these sl n + 2 -modules to be simple are determined. This leads to a cl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c1e81a755b425b368b18aa28595268f8
https://doi.org/10.1016/j.jalgebra.2018.01.019
https://doi.org/10.1016/j.jalgebra.2018.01.019
Publikováno v:
Journal of Algebra. 501:458-472
Let n > 1 be an integer, α ∈ C n , b ∈ C , and V a gl n -module. We define a class of weight modules F b α ( V ) over sl n + 1 using the restriction of modules of tensor fields over the Lie algebra of vector fields on n-dimensional torus. In th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e4a1c6721b113b5728f789884b073cf1
https://doi.org/10.1016/j.jalgebra.2017.12.029
https://doi.org/10.1016/j.jalgebra.2017.12.029