论文标题
海藻上的常规功能谎言代数
Regular functionals on seaweed Lie algebras
论文作者
论文摘要
lie代数$ \ mathfrak {g} $的索引由Ind $ \ Mathfrak {G} = $ $ \ $ \ min_ {f \ in \ Mathfrak {g}^*} \ dim（\ ker（b_f）） $ b_f（x，y）= f（[x，y]）$是相关的偏斜kirillov表单。我们开发了一个广泛的一般框架，用于针对$ \ Mathfrak {gl}（n）$的海藻亚代代代代他的常规（索引实现）功能的明确构建，而经典的lie代数：$ a_n = \ mathfrak {slfrak {sl}（n+1）（n+1），$ $ b_n = \ mathfrak { $ C_N = \ Mathfrak {Sp}（2n）$。到目前为止，此问题一直在$ \ mathfrak {gl}（n）$以及所有经典类型中打开。
The index of a Lie algebra $\mathfrak{g}$ is defined by ind $\mathfrak{g}=$ $\min_{f\in \mathfrak{g}^*}\dim(\ker (B_f))$, where $f$ is an element of the linear dual $\mathfrak{g}^*$ and $B_f(x,y)=f([x,y])$ is the associated skew-symmetric Kirillov form. We develop a broad general framework for the explicit construction of regular (index realizing) functionals for seaweed subalgebras of $\mathfrak{gl}(n)$ and the classical Lie algebras: $A_n=\mathfrak{sl}(n+1),$ $B_n=\mathfrak{so}(2n+1)$, and $C_n=\mathfrak{sp}(2n)$. Until now, this problem has remained open in $\mathfrak{gl}(n)$ -- and in all the classical types.
