The authors have recently completed a partial classification of the ten-dimensional real Lie algebras that have the non-trivial Levi decomposition, namely, for such algebras whose semi-simple factor is so(3). In the p...The authors have recently completed a partial classification of the ten-dimensional real Lie algebras that have the non-trivial Levi decomposition, namely, for such algebras whose semi-simple factor is so(3). In the present paper, we obtain a matrix representation for each of these Lie algebras. We are able to find such representations by exploiting properties of the radical, principally, when it has a trivial center, in which case we can obtain such a representation by restricting the adjoint representation. Another important subclass of algebras is where the radical has a codimension one abelian nilradical and for which a representation can readily be found. In general, finding matrix representations for abstract Lie algebras is difficult and there is no algorithmic process, nor is it at all easy to program by computer, even for algebras of low dimension. The present paper represents another step in our efforts to find linear representations for all the low dimensional abstract Lie algebras.展开更多
We describe the establishing process for the Boson-Fermion algebra of OSP(1, 2) starting from the fundamental Wigner operators of OSP(1, 2), and study its structure feature and representation theory. We also give the ...We describe the establishing process for the Boson-Fermion algebra of OSP(1, 2) starting from the fundamental Wigner operators of OSP(1, 2), and study its structure feature and representation theory. We also give the Boson-Fermion representation of OSP (1, 2), which is an infinite dimensional and grade star representation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
文摘The authors have recently completed a partial classification of the ten-dimensional real Lie algebras that have the non-trivial Levi decomposition, namely, for such algebras whose semi-simple factor is so(3). In the present paper, we obtain a matrix representation for each of these Lie algebras. We are able to find such representations by exploiting properties of the radical, principally, when it has a trivial center, in which case we can obtain such a representation by restricting the adjoint representation. Another important subclass of algebras is where the radical has a codimension one abelian nilradical and for which a representation can readily be found. In general, finding matrix representations for abstract Lie algebras is difficult and there is no algorithmic process, nor is it at all easy to program by computer, even for algebras of low dimension. The present paper represents another step in our efforts to find linear representations for all the low dimensional abstract Lie algebras.
文摘We describe the establishing process for the Boson-Fermion algebra of OSP(1, 2) starting from the fundamental Wigner operators of OSP(1, 2), and study its structure feature and representation theory. We also give the Boson-Fermion representation of OSP (1, 2), which is an infinite dimensional and grade star representation
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).
