Leibniz central extension on centerless twisted Schrödinger-Virasoro algebra
Copyright policy )Leibniz central extension on centerless twisted Schrödinger-Virasoro algebra
The centerless twisted Schrödinger-Virasoro Lie algebra \(\mathcal L\) has a basis \(\{ L_n, Y_n, M_n, n\in \mathbb Z\}\) such that \([L_n,L_m]=(m-n)L_{n+m}, ~[L_n,Y_m]=(m-\frac{n}{2})Y_{n+m}, ~[L_n, M_p]= pM_{n+p}, ~[Y_n, Y_m]=(m-n)M_{n+m}\) and other brackets are equal to zero. It is proved that the second Leibniz cohomology group of \(\mathcal L\) is one-dimensional and generated by Virasoro Leibniz cocycle \(\xi \), \(\xi (L_n, L_m)=\frac{n^3-n}{12}\delta _{m,-n}, \xi \) equals zero on other pairs of basic vectors.
- University of Science and Technology of China China (People's Republic of)
- Changshu Institute of Technology China (People's Republic of)
- Shanghai Jiao Tong University China (People's Republic of)
Virasoro and related algebras, Leibniz 2-cocycle, Leibniz cohomology group, Cohomology of Lie (super)algebras, Homological methods in Lie (super)algebras, Leibniz algebras, Schrödinger-Virasoro algebra
Virasoro and related algebras, Leibniz 2-cocycle, Leibniz cohomology group, Cohomology of Lie (super)algebras, Homological methods in Lie (super)algebras, Leibniz algebras, Schrödinger-Virasoro algebra
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