Gelfand–Kirillov Dimension and Local Finiteness of Jordan Superpairs Covered by Grids and Their Associated Lie Superalgebras
Gelfand–Kirillov Dimension and Local Finiteness of Jordan Superpairs Covered by Grids and Their Associated Lie Superalgebras
复制标题
网格及其相关李超代数覆盖的 Jordan 超对的 Gelfand-Kirilov 维数和局部有限性
DOI：
10.1081/agb-120037212
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
E. Neher
中科院分区：
文献类型：
--
作者：
E. García;E. Neher
本文证明了由3-分次不可约根系分次的L李超代数的Gelfand-Kirillov维度等于其坐标超代数A的Gelfand-Kirillov维度，且L局部有限的充要条件是A是局部有限的。由于这些李超代数是由一个连通格子覆盖的Jordan超对的Tits-Kantor-Koecher超代数的覆盖，我们结合另外两个结果得到了我们的定理。首先，我们研究了这些李超代数与其相应的Jordan超对之间的Gelfand-Kirillov维数和局部有限性的转移，其次，我们证明了Jordan超对的类似结果：连通格子覆盖的Jordan超对V的Gelfand-Kirillov维度与其坐标超代数A的Gelfand-Kirillov维度重合，且V局部有限的充要条件是A是局部有限的。
Abstract In this paper we show that a Lie superalgebra L graded by a 3-graded irreducible root system has Gelfand–Kirillov dimension equal to the Gelfand–Kirillov dimension of its coordinate superalgebra A, and that L is locally finite if and only A is so. Since these Lie superalgebras are coverings of Tits–Kantor–Koecher superalgebras of Jordan superpairs covered by a connected grid, we obtain our theorem by combining two other results. Firstly, we study the transfer of the Gelfand–Kirillov dimension and of local finiteness between these Lie superalgebras and their associated Jordan superpairs, and secondly, we prove the analogous result for Jordan superpairs: the Gelfand–Kirillov dimension of a Jordan superpair V covered by a connected grid coincides with the Gelfand– Kirillov dimension of its coordinate superalgebra A, and V is locally finite if and only if A is so.