Blocks of Birman–Murakami–Wenzl Algebras
Blocks of Birman–Murakami–Wenzl Algebras
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DOI：
10.1093/imrn/rnq083
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发表时间：
2010-04
影响因子：
1
通讯作者：
H. Rui;Mei Si
中科院分区：
文献类型：
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作者：
H. Rui;Mei Si
Birman，Wenzl [3]和Murakami [19]独立地引入了一类有限维代数，它们被称为Birman-Murakami-Wenzl代数或BMW代数。当基域κ包含可逆的r和q，使得q 2的乘法阶o（q 2）严格大于n，且κ的特征不为2时，我们确定了的胞腔模Δ（1，λ）的结构，其中λ是n −2的任意划分.特别是，我们计算了Δ（1，λ）的简单头的维度。考克斯，De Visscher和Martin在[5]中对Brauer代数B n的块进行了分类.我们解决了上述领域κ上的类似问题。作为一个副产品，我们给出了一个准则，每个模是等于它的简单头上的任意域。
Birman, Wenzl [3], and independently Murakami [19] introduced a class of finite dimensional algebras , which are known as the Birman–Murakami–Wenzl algebras or BMW algebras. When the ground field κ contains invertible r and q such that o(q 2 ), the multiplicative order of q 2 , is strictly greater than n, and char(κ), the characteristic of κ is not 2, we determine the structure of the cell module Δ(1, λ) of , where λ is any partition of n −2. In particular, we compute the dimension of the simple head of Δ(1, λ). Cox, De Visscher, and Martin have classified the blocks of Brauer algebras B n in characteristic zero [5]. We solve the similar problem for over the aforementioned field κ. As a by-product, we give a criterion for each module of being equal to its simple head over an arbitrary field.