In this paper we study the homology and cohomology groups of the super Schrodinger algebra S(1/1)in(1+l)-dimensional spacetime.We explicitly compute the homology groups of S(1/1)with coefficients in the trivial module...In this paper we study the homology and cohomology groups of the super Schrodinger algebra S(1/1)in(1+l)-dimensional spacetime.We explicitly compute the homology groups of S(1/1)with coefficients in the trivial module.Then using duality,we finally obtain the dimensions of the cohomology groups of S(1/1)with coefficients in the trivial module.展开更多
In this paper, we study Leibniz algebras with a non-degenerate Leibniz- symmetric fl-invariant bilinear form B, such a pair （g, B） is called a quadratic Leibniz algebra. Our first result generalizes the notion of d...In this paper, we study Leibniz algebras with a non-degenerate Leibniz- symmetric fl-invariant bilinear form B, such a pair （g, B） is called a quadratic Leibniz algebra. Our first result generalizes the notion of double extensions to quadratic Leibniz algebras. This notion was introduced by Medina and Revoy to study quadratic Lie alge- bras. In the second theorem, we give a sufficient condition for a quadratic Leibniz algebra to be a quadratic Leibniz algebra by double extension.展开更多
文摘In this paper we study the homology and cohomology groups of the super Schrodinger algebra S(1/1)in(1+l)-dimensional spacetime.We explicitly compute the homology groups of S(1/1)with coefficients in the trivial module.Then using duality,we finally obtain the dimensions of the cohomology groups of S(1/1)with coefficients in the trivial module.
基金Supported by the National Natural Science Foundation of China （10571119, 10671027, 11271056, 11271284）, the Foundation of Jiangsu Educational Committee, the Fundamental Research Funds for the Central Universities and the Youth Scholars of Shanghai Higher Education Institutions （Gr~nt No.ZZHY14026）.
文摘In this paper, we study Leibniz algebras with a non-degenerate Leibniz- symmetric fl-invariant bilinear form B, such a pair （g, B） is called a quadratic Leibniz algebra. Our first result generalizes the notion of double extensions to quadratic Leibniz algebras. This notion was introduced by Medina and Revoy to study quadratic Lie alge- bras. In the second theorem, we give a sufficient condition for a quadratic Leibniz algebra to be a quadratic Leibniz algebra by double extension.
