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.
In this paper, we study an infinite-dimensional Lie algebra Bq, called the q-analog Klein bottle Lie algebra. We show that Bq is a finitely generated simple Lie algebra with a unique （up to scalars） symmetric invari...In this paper, we study an infinite-dimensional Lie algebra Bq, called the q-analog Klein bottle Lie algebra. We show that Bq is a finitely generated simple Lie algebra with a unique （up to scalars） symmetric invariant bilinear form. The derivation algebra and the universal central extension of Bq are also determined.展开更多
In this paper, an explicit determinant formula is given for the Verma modules over the Lie algebra W(2, 2). We construct a natural realization of a certain vaccum module for the algebra W(2, 2) via the Weyl vertex alg...In this paper, an explicit determinant formula is given for the Verma modules over the Lie algebra W(2, 2). We construct a natural realization of a certain vaccum module for the algebra W(2, 2) via the Weyl vertex algebra. We also describe several results including the irreducibility, characters and the descending filtrations of submodules for the Verma module over the algebra W(2, 2).展开更多
基金supported by financial support from the National Key Research and Development Program of China(2021YFF1200200)the National Natural Science Foundation of China(22161132008)+2 种基金the Natural Science Foundation of Shanghai,China(19520714100 and 19ZR1475800)the Starry Night Science Fund of Zhejiang University Shanghai Institute for Advanced Study(SNZJU-SIAS-006)the Natural Science Foundation of Zhejiang Province(LQ21C050001)。
基金supported by the National Natural Science Foundation of China(Nos.11871249,11371134)the Natural Science Foundation of Zhejiang Province(No.LZ14A010001)the Shanghai Natural Science Foundation(No.16ZR1425000)
文摘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.
基金The first author was supported in part by the NSFC （10931006, 10871125） and the Innovation Program of Shanghai Municipal Education Commission （11ZZ18）. The second author was supported by the NSFC （11326060）. The third author was supported in part by the NSFC （11101285, 11026042, 11071068）, the Shanghai Natural Science Foundation （11ZR1425900）, the Innovation Program of Shanghai Municipal Education Commission （11YZ85）, the Academic Discipline Project of Shanghai Normal University （DZL803） and ZJNSF （Y6100148）.
文摘In this paper, we study an infinite-dimensional Lie algebra Bq, called the q-analog Klein bottle Lie algebra. We show that Bq is a finitely generated simple Lie algebra with a unique （up to scalars） symmetric invariant bilinear form. The derivation algebra and the universal central extension of Bq are also determined.
基金supported by National Natural Science Foundation of China (Grant Nos. 11271056, 11671056 and 11101030)National Science Foundation of Jiangsu (Grant No. BK20160403)+3 种基金National Science Foundation of Zhejiang (Grant Nos. LQ12A01005 and LZ14A010001)National Science Foundation of Shanghai (Grant No. 16ZR1425000)Beijing Higher Education Young Elite Teacher ProjectMorningside Center of Mathematics
文摘In this paper, an explicit determinant formula is given for the Verma modules over the Lie algebra W(2, 2). We construct a natural realization of a certain vaccum module for the algebra W(2, 2) via the Weyl vertex algebra. We also describe several results including the irreducibility, characters and the descending filtrations of submodules for the Verma module over the algebra W(2, 2).
