论文标题
非线性实现超级级别的谎言
Nonlinear realisations of Lie superalgebras
论文作者
论文摘要
For any decomposition of a Lie superalgebra $\mathcal G$ into a direct sum $\mathcal G=\mathcal H\oplus\mathcal E$ of a subalgebra $\mathcal H$ and a subspace $\mathcal E$, without any further resctrictions on $\mathcal H$ and $\mathcal E$, we construct a nonlinear realisation of $ \ MATHCAL E $上的$ \ Mathcal G $。结果将kantor的定理从谎言代数为superalgebras。当$ \ Mathcal G $是一个差分级的Lie代数时，我们表明它为相关的$ l_ \ infty $ -Algebra提供了构造。
For any decomposition of a Lie superalgebra $\mathcal G$ into a direct sum $\mathcal G=\mathcal H\oplus\mathcal E$ of a subalgebra $\mathcal H$ and a subspace $\mathcal E$, without any further resctrictions on $\mathcal H$ and $\mathcal E$, we construct a nonlinear realisation of $\mathcal G$ on $\mathcal E$. The result generalises a theorem by Kantor from Lie algebras to Lie superalgebras. When $\mathcal G$ is a differential graded Lie algebra, we show that it gives a construction of an associated $L_\infty$-algebra.
