论文标题
有限维简单的Jordan Superalgebra $ \ Mathcal {d} _ {t} $，$ t \ neq 0 $
Second cohomology group of the finite-dimensional simple Jordan superalgebra $\mathcal{D}_{t}$, $t\neq 0$
论文作者
论文摘要
Jordan Superalgebra $ \ Mathcal {D} _ {T} $，$ T \ neq 0 $的第二个共同体学组（SCG）是通过使用常规SuperBimodule $ \ MATHRM {REG} \ MATHCAL {D MATHCAL {D} _t $的系数来计算的。与代数相反，由于Wedderburn分解定理\ cite {faber1}引起的非分类，该组是不平凡的。首先，为了计算Jordan Superalgebra的SCG，我们使用Jordan Superalgebra和Jordan Superalgebra代表的拆分弹道扩展。我们证明了满足双线性形成$ h $的条件，这些$ h $确定了约旦超级甲壳虫的SCG。我们使用这些来计算Jordan Superalgebra $ \ Mathcal {D} _ {T} $，$ T \ neq 0 $的SCG。最后，我们证明$ \ Mathcal {h}^2（\ Mathcal {d} _ {t}，\ textrm {reg} \ Mathcal {d} _ {t} _ {t}）= 0 \ oplus \ oplus \ mathbb {f}^2 $，$ t $，$ t \ t \ neq 0 $。
The second cohomology group (SCG) of the Jordan superalgebra $\mathcal{D}_{t}$, $t\neq 0$, is calculated by using the coefficients which appear in the regular superbimodule $\mathrm{Reg}\mathcal{D}_t$. Contrary to the case of algebras, this group is nontrivial thanks to the non-splitting caused by the Wedderburn Decomposition Theorem \cite{Faber1}. First, to calculate the SCG of a Jordan superalgebra we use split-null extension of the Jordan superalgebra and the Jordan superalgebra representation. We prove conditions that satisfy the bilinear forms $h$ that determine the SCG in Jordan superalgebras. We use these to calculate the SCG for the Jordan superalgebra $\mathcal{D}_{t}$ , $t\neq 0$. Finally, we prove that $\mathcal{H}^2(\mathcal{D}_{t}, \textrm{Reg}\mathcal{D}_{t})=0\oplus\mathbb{F}^2$, $t\neq 0$.
