论文标题
B，C和D的Lie Poset代数的指数和频谱
The index and spectrum of Lie poset algebras of type B, C, and D
论文作者
论文摘要
在本文中，我们定义了B型，C和D的posets。这些POSET编码某些位于三角形和对角线矩阵代数之间的某些代数的基质形式。有趣的是，这种类型B，C和D Lie Poset代数可能与Reiner的绘制概念有关。我们的主要关注点是B，C和D型Poset代数的索引和光谱理论。对于一个重要的限制类别，我们开发了组合索引公式，尤其是特征在于与Frobenius Lie代数相对应的POSET。在后一种情况下，我们表明频谱是二进制的。也就是说，由等于0和1的数字组成。
In this paper, we define posets of types B, C, and D. These posets encode the matrix forms of certain Lie algebras which lie between the algebras of upper-triangular and diagonal matrices. Interestingly, such type-B, C, and D Lie poset algebras can be related to Reiner's notion of a parset. Our primary concern is the index and spectral theories of type-B, C, and D Lie poset algebras. For an important restricted class, we develop combinatorial index formulas and, in particular, characterize posets corresponding to Frobenius Lie algebras. In this latter case we show that the spectrum is binary; that is, consists of an equal number of 0's and 1's.
