We quantize the W-algebra W（2,2）, whose Verma modules, Harish-Chandra modules, irreducible weight modules and Lie bialgebra structures have been investigated and determined in a series of papers recently.
The q-deformation of W（2, 2） Lie algebra is well defined based on a realization of this Lie algebra by using the famous bosonic and fermionic oscillators in physics. Furthermore, the quantum group structures on the ...The q-deformation of W（2, 2） Lie algebra is well defined based on a realization of this Lie algebra by using the famous bosonic and fermionic oscillators in physics. Furthermore, the quantum group structures on the q-deformation of W（2, 2） Lie algebra are completely determined. Finally, the 1-dimensional central extension of the q-deformed W（2, 2） Lie algebra is studied, which turns out to be coincided with the conventional W（2, 2） Lie algebra in the q → 1 limit.展开更多
This paper aims to study low dimensional cohomology of Hom-Lie algebras and the qdeformed W（2, 2） algebra. We show that the q-deformed W（2, 2） algebra is a Hom-Lie algebra. Also,we establish a one-to-one correspon...This paper aims to study low dimensional cohomology of Hom-Lie algebras and the qdeformed W（2, 2） algebra. We show that the q-deformed W（2, 2） algebra is a Hom-Lie algebra. Also,we establish a one-to-one correspondence between the equivalence classes of one-dimensional central extensions of a Hom-Lie algebra and its second cohomology group, leading us to determine the second cohomology group of the q-deformed W（2, 2） algebra. In addition, we generalize some results of derivations of finitely generated Lie algebras with values in graded modules to Hom-Lie algebras.As application, we compute all αk-derivations and in particular the first cohomology group of the q-deformed W（2, 2） algebra.展开更多
In the present paper, we investigate the dual Lie coalgebras of the centerless W(2,2) algebra by studying the maximal good subspaces. Based on this, we construct the dual Lie bialgebra structures of the centerless W(2...In the present paper, we investigate the dual Lie coalgebras of the centerless W(2,2) algebra by studying the maximal good subspaces. Based on this, we construct the dual Lie bialgebra structures of the centerless W(2,2) Lie bialgebra. As by-products, four new infinite dimensional Lie algebras are obtained.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
For any complex parameters a, b, let W（a, b） be the Lie algebra with basis {Li, Hi｜i ∈ Z} and relations [Li,Lj] = （j - i）Li＋j, [Li,Hj] = （a ＋ j ＋ bi）Hi＋j and [Hi, Hi] = 0. In this paper, we construct the W...For any complex parameters a, b, let W（a, b） be the Lie algebra with basis {Li, Hi｜i ∈ Z} and relations [Li,Lj] = （j - i）Li＋j, [Li,Hj] = （a ＋ j ＋ bi）Hi＋j and [Hi, Hi] = 0. In this paper, we construct the W（a, b） conformal algebra for some a, b and its conformal module of rank one.展开更多
We study conformal biderivations of a Lie conformal algebra.First,we give the definition of a conformal biderivation.Next,we determine the conformal biderivations of loop W(a,b)Lie conformal algebra,loop Virasoro Lie ...We study conformal biderivations of a Lie conformal algebra.First,we give the definition of a conformal biderivation.Next,we determine the conformal biderivations of loop W(a,b)Lie conformal algebra,loop Virasoro Lie conformal algebra,and Virasoro Lie conformal algebra.Especially,all conformal biderivations on Virasoro Lie conformal algebra are inner conformal biderivations.展开更多
基金Supported by NSF＇of China （Grant Nos. 10825101, 10926166）, Special Grade of the Financial Support from China Postdoctoral Science Foundation （Grant No. 201003326） and the Natural Science Research Project for Higher Institutions of Jiangsu Province （Grant No. 09KJB110001）
文摘We quantize the W-algebra W（2,2）, whose Verma modules, Harish-Chandra modules, irreducible weight modules and Lie bialgebra structures have been investigated and determined in a series of papers recently.
基金Supported by National Natural Science Foundation of China (Grant No. 10825101)
文摘The q-deformation of W（2, 2） Lie algebra is well defined based on a realization of this Lie algebra by using the famous bosonic and fermionic oscillators in physics. Furthermore, the quantum group structures on the q-deformation of W（2, 2） Lie algebra are completely determined. Finally, the 1-dimensional central extension of the q-deformed W（2, 2） Lie algebra is studied, which turns out to be coincided with the conventional W（2, 2） Lie algebra in the q → 1 limit.
基金Supported by China Scholarship Council(Grant No.201206125047)China Postdoctoral Science Foundation Funded Project(Grant No.2012M520715)the Fundamental Research Funds for the Central Universities(Grant No.HIT.NSRIF.201462)
文摘This paper aims to study low dimensional cohomology of Hom-Lie algebras and the qdeformed W（2, 2） algebra. We show that the q-deformed W（2, 2） algebra is a Hom-Lie algebra. Also,we establish a one-to-one correspondence between the equivalence classes of one-dimensional central extensions of a Hom-Lie algebra and its second cohomology group, leading us to determine the second cohomology group of the q-deformed W（2, 2） algebra. In addition, we generalize some results of derivations of finitely generated Lie algebras with values in graded modules to Hom-Lie algebras.As application, we compute all αk-derivations and in particular the first cohomology group of the q-deformed W（2, 2） algebra.
基金Supported by NSF grant of China and NSF grant of Shandong Province(Grant Nos.11431010,11671056,ZR2013AL013 and ZR2014AL001)
文摘In the present paper, we investigate the dual Lie coalgebras of the centerless W(2,2) algebra by studying the maximal good subspaces. Based on this, we construct the dual Lie bialgebra structures of the centerless W(2,2) Lie bialgebra. As by-products, four new infinite dimensional Lie algebras are obtained.
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).
基金Supported by National Natural Science Foundation of China(11971315,11871249)Scientific Research Project of Huzhou University(The structures and representations of several types of infinite dimensional Lie algebras)
文摘For any complex parameters a, b, let W（a, b） be the Lie algebra with basis {Li, Hi｜i ∈ Z} and relations [Li,Lj] = （j - i）Li＋j, [Li,Hj] = （a ＋ j ＋ bi）Hi＋j and [Hi, Hi] = 0. In this paper, we construct the W（a, b） conformal algebra for some a, b and its conformal module of rank one.
基金supported by the National Natural Science Foundation of China(Grant Nos.11771069,12071405,11301109)China Postdoctoral Science Foundation(2020M682272)the Natural Science Foundation of Hennan Province(212300410120).
文摘We study conformal biderivations of a Lie conformal algebra.First,we give the definition of a conformal biderivation.Next,we determine the conformal biderivations of loop W(a,b)Lie conformal algebra,loop Virasoro Lie conformal algebra,and Virasoro Lie conformal algebra.Especially,all conformal biderivations on Virasoro Lie conformal algebra are inner conformal biderivations.
