论文标题
局部nilpotent无限维谎言代数的轨道方法
The orbit method for locally nilpotent infinite-dimensional Lie algebras
论文作者
论文摘要
令$ \ mathfrak {n} $为本地nilpotent nilpotent infinite-dimenition lie lie代数，超过$ \ mathbb {c} $。令$ \ mathrm {u}（\ mathfrak {n}）$和$ \ mathrm {s}（\ mathfrak {n}）$是其通用的代数及其对称代数。考虑$ \ mathrm {u}（\ mathfrak {n}）$的原始光谱上的雅各布森拓扑，以及$ \ mathrm {s}（s s}（\ mathfrak {n}）$ \ mathrm {s}的原始泊松光谱上的泊松拓扑。我们在相应的拓扑空间之间提供同构（在点的级别上，它在$ \ mathrm {u}（\ Mathfrak {n}）$和$ \ mathrm {s}（\ mathfrak {n}）$之间提供了培养。我们还表明，从正确选择的拓扑中的开放集中，$ \ mathrm {s}（\ mathfrak {n}）$的所有原始理想都是由其与Poisson Center的交叉点生成的。在假设$ \ mathfrak {n} $是一个nil-dynkin lie代数的假设下，我们给出了两个原始理想的标准$ i（λ）\ subset \ subset \ mathrm {s}（\ mathfrak {n}）$ $λ\ in \ mathfrak {n}^*$，为非零。这些结果中的大多数概括了有关有限维nilpotent lie代数的原始和泊松谱的已知事实（但请注意，对于有限维nilpotent lie lie代数代数代数所有原始理想$ i（λ）$，$ j（λ）$是非零的）。
Let $\mathfrak{n}$ be a locally nilpotent infinite-dimensional Lie algebra over $\mathbb{C}$. Let $\mathrm{U}(\mathfrak{n})$ and $\mathrm{S}(\mathfrak{n})$ be its universal enveloping algebra and its symmetric algebra respectively. Consider the Jacobson topology on the primitive spectrum of $\mathrm{U}(\mathfrak{n})$ and the Poisson topology on the primitive Poisson spectrum of $\mathrm{S}(\mathfrak{n})$. We provide a homeomorphism between the corresponding topological spaces (on the level of points, it gives a bijection between the primitive ideals of $\mathrm{U}(\mathfrak{n})$ and $\mathrm{S}(\mathfrak{n})$). We also show that all primitive ideals of $\mathrm{S}(\mathfrak{n})$ from an open set in a properly chosen topology are generated by their intersections with the Poisson center. Under the assumption that $\mathfrak{n}$ is a nil-Dynkin Lie algebra, we give two criteria for primitive ideals $I(λ)\subset\mathrm{S}(\mathfrak{n})$ and $J(λ)\subset\mathrm{U}(\mathfrak{n})$, $λ\in\mathfrak{n}^*$, to be nonzero. Most of these results generalize the known facts about primitive and Poisson spectrum for finite-dimensional nilpotent Lie algebras (but note that for a finite-dimensional nilpotent Lie algebra all primitive ideals $I(λ)$, $J(λ)$ are nonzero).
