一类特殊的Koszul Calabi-Yau DG代数

假设一个连通上链DG代数A的基分次代数A~#或者同调分次代数H(A)是由一次元素x,y生成的代数kx,y/(xy+yx).本文证明A是Koszul Calabi-Yau DG代数.     

弱Hopf代数上的Militaru-Stefan提升定理

本文研究了弱Hopf-Galois扩张的扩张模.利用忠实平坦的弱Hopf-Galois扩张理论,研究了弱Hopf代数上的Militaru-Stefan提升定理,推广了文献[10]中的相应结果.进一步地,通过诱导模的自同态环的cleft扩张刻画了弱稳定模.     

代数的张量积的同调满同态的构造

利用已知的代数的同调满同态来构造其张量积代数的同调满同态.设A,B,C,D是域k上的有限维代数,如果环同态f:A→C和g:B→D是环的同调满同态,则fg:AB→CD也是环的同调满同态.     

Locally symmetric left invariant Riemannian metrics on 3‐dimensional Lie groups

In this paper, we use the powerful tool Milnor bases to determine all the locally symmetric left invariant Riemannian metrics up to automorphism, on 3‐dimensional connected and simply connected Lie groups, by solving system of polynomial equations of constants structure of each Lie algebra . Moreover, we show that E ₀(2) is the only 3‐dimensional Lie group with locally symmetric left invariant Riemannian metrics which are not symmetric.     

On parakähler Hom-Lie algebras and Hom-left-symmetric bialgebras

In this paper, the parakähler Hom-Lie algebras or phase space of Hom-Lie algebras in terms of Hom-left-symmetric algebras are studied. A structure theory of parakähler Hom-Lie algebras in terms of matched pairs of Hom-Lie algebras is also presented. Besides, the bimodules of Hom-left-symmetric algebras are investigated. Furthermore, Hom-left-symmetric bialgebra which is precisely equivalent to parakähler Hom-Lie algebra is introduced. Especially, the coboundary Hom-left-symmetric bialgebra is considered.     

Structures of the twisted N = 1 Schrödinger–Neveu–Schwarz algebra

In this paper, we determine the universal central extension, derivation algebra and automorphism group of the twisted N = 1 Schrödinger–Neveu–Schwarz algebra. Furthermore, we generalize these results to the generalized twisted N = 1 Schrödinger–Neveu–Schwarz algebra in the final section.     

On classification of four-dimensional nilpotent Leibniz algebras

Leibniz algebras are certain generalization of Lie algebras. In this paper, we give the classification of four-dimensional non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of bilinear forms and some other techniques to obtain our result.