The blob algebra in positive characteristic
The blob algebra in positive characteristic
复制标题
正特征的斑点代数
DOI：
10.1016/s0021-8693(03)00260-6
复制
发表时间：
2003
影响因子：
0.9
通讯作者：
Paul Martin
中科院分区：
文献类型：
--
作者：
A. Cox;J. Graham;Paul Martin
blob代数最初是在[1]中在统计力学的背景下引入的，作为普通Temperley-Lieb代数的推广。在[2]中，这些代数的块被确定，连同标准模的结构（在拟遗传意义下），在任何特征为零的域上。本文给出了正特征的相应结果，blob代数可以定义为B型Hecke代数HB（n）的商，就像普通Temperley-Lieb代数TLA（n）可以等同于A型Hecke代数HA（n）的商一样。由于这个原因，我们将把blob代数看作TLA（n）的B型类似物，并将其表示为TLB（n）。这个代数与Tom Dieck [3]定义的代数TBn密切相关。
The blob algebra was originally introduced in [1] in the context of statistical mechanics, as a generalisation of the ordinary Temperley-Lieb algebra. In [2] the blocks of these algebras were determined, together with the structure of the standard modules (in the quasi-hereditary sense), over any field of characteristic zero. In this paper we shall determine corresponding results in positive characteristic.The blob algebra can be defined as a quotient of the type B Hecke algebra HB (n), much as the ordinary Temperley-Lieb algebra TLA (n) can be identified with a quotient of the type A Hecke algebra HA (n). For this reason we shall consider the blob algebra to be the type B analogue of TLA (n), and denote it by TLB (n). This algebra is closely related to the algebra TBn defined by tom Dieck [3].