格子SL2(5)(Sp4(3)xC3.2)。2
《格目录》中的一个条目,该目录是
Gabriele Nebe,亚琛RWTH大学(nebe@math.rwth-aachen.de)和
尼尔·J·A·斯隆(njasloane@gmail.com)
上次修改时间:2014年7月18日星期五13:13:52 CEST
索引文件|缩写
此文件的内容
名称
尺寸
GRAM(浮点或整数GRAM矩阵)
除数(初等除数)
最小_形式
亲吻_编号
组订单(_O)
发电机组
属性
参考文献
笔记
URL(指向此晶格的其他站点的链接)
最后一行
-
名称
SL2(5)(Sp4(3)xC3.2).2
-
尺寸
32
-
GRAM(浮点或整数GRAM矩阵)
32 0个
12
3 12个
6 2 12
3 2 6 12
3 0 3 2 12
6 6 3 6 -1 12
0 4 3 6 2 6 12
6 3 3 6 2 6 6 12
3-1 6 6 4 0 3 6 12
3 4 4 6 0 4 2 3 2 12
3 4 4 6 2 4 2 3 2 6 12
6 3 0 3 4 3 3 6 0 3 3 12
3 0 3 2 6 -1 2 2 4 1 2 4 12
3 2 4 6 2 4 2 3 2 6 6 3 2 12
3 1 3 1 6 1 4 4 2 0 0 2 6 2 12
3 4 4 6 1 4 2 3 2 6 6 3 2 6 0 12
3 4 4 6 1 4 2 3 2 6 6 3 0 6 0 0 12
3 0 3 2 6 -1 2 2 4 2 2 4 6 2 6 0 2 12
2 2 6 4 0 2 3 1 2 6 4 -1 3 2 0 4 2 0 12
3 2 3 2 6 -1 2 2 4 0 0 4 6 1 6 0 0 6 0 12
4 2 2 2 0 4 3 1 -1 2 0 2 3 0 3 0 1 3 4 3 12
3 6 2 2 0 6 4 3 -1 6 2 3 1 4 0 2 4 -1 3 0 4 12
3 6 2 2 2 6 4 3 -1 4 0 3 1 0 2 2 2 0 2 1 4 6 12
4 3 1 3 4 3 3 6 2 3 3 6 4 0 2 3 0 4 1 4 1 3 3 12
3 6 2 2 1 6 4 3 -1 4 2 3 1 0 2 4 0 1 2 1 4 6 6 6 12
4 4 2 2 0 4 3 1 -1 3 2 2 3 1 0 2 1 0 6 0 6 6 4 1 4 12
3 2 3 1 6 1 4 4 2 -1 1 2 6 0 6 -1 0 6 3 6 3 2 2 6 3 3 12
0 4 3 4 4 2 6 3 2 2 4 3 4 0 2 2 0 4 3 4 3 4 4 6 6 3 6 12
0 4 3 4 0 2 6 3 2 4 0 3 2 0 2 0 2 4 3 4 3 2 2 3 2 0 2 6 12
4 3 1 3 4 3 6 2 0 6 0 2 3 0 2 0 4 2 0 3 3 3 0 2 3 3 12
4 0 1 3 6 3 3 6 2 0 3 6 2 3 4 3 0 4 0 2 0 0 0 6 3 0 4 3 0 6 12
6 3 4 3 0 3 0 4 2 6 3 2 3 3 0 3 3 0 6 0 2 3 3 4 3 6 3 0 0 0 0 12
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除数(初等除数)
1^16 15^16
-
最小_形式
12
-
亲吻_编号
4800
-
组订单(_O)
2^11 * 3^6 * 5^2
-
发电机组
5
32
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1
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1 0 0 0 1 -1 1 2 -2 0 0 -2 1 0 -2 0 0 1 0 1 0 0 0 0 0 0 -1 -1 0 0 0 0
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0 -1 -1 0 0 0 -1 -1 1 -2 2 0 -1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 -1 2 0 0 1
0 0 0 0 1 0 0 1 -1 0 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0
1-1-1 0-1 0 0-1 1-1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0-1 1 0 0 0 0
-1 0 0 0 0 1 -1 -1 1 0 0 1 -1 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 1
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0 -1 -1 -1 0 1 0 -1 1 -1 0 1 -1 0 1 1 1 0 1 0 0 0 0 0 0 -1 0 1 0 0 -1 1
0 1 1 0 1 0 1 3 -3 1 -1 -2 2 0 -2 -1 0 1 0 1 0 -1 -1 0 0 0 -2 0 -1 0 0 0
1 0 -1 1 0 -1 1 0 -1 -1 0 -1 0 0 0 0 0 1 1 0 0 1 0 0 0 -1 -1 0 0 0 0 1
0 -1 -1 -1 0 0 0 -1 1 -1 1 0 -1 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1
1 1 0 0 0 -1 1 1 -1 2 -1 -1 1 1 -1 -1 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0 0 -1
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0 -1 -1 -1 0 0 0 -1 1 -1 0 0 -1 -1 1 2 2 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1
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1 0 0 1 1 -2 1 3 -3 0 0 -2 1 0 -2 0 0 1 0 1 0 0 0 -1 1 0 -1 -1 0 0 0 0
0 -1 0 0 0 0 0 -1 0 0 1 0 0 -1 0 1 0 0 -1 0 0 1 0 -1 0 0 1 -1 1 1 0 1
0 -1 -1 -1 -1 0 0 -2 2 -1 1 1 -1 0 1 1 1 -1 0 0 0 0 1 0 0 0 1 0 1 0 0 1
32
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0 0 0 0 0 0 0 1 -1 0 0 -1 1 0 -1 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 1 0 0
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0 0 0-1 0 1 1 0 1-1 0 0-1 0 1 1 0 0 0 0 0-1 0-1 0 0 1 0 0 0 0
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1 0 -1 0 0 0 0 0 0 -1 0 -1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
-2 0 0 -1 0 3 -1 -1 1 0 -1 1 0 -1 1 1 1 0 0 0 0 0 -1 0 -1 0 0 1 0 0 0 1
-2 0 0 -1 0 3 -1 -3 3 0 -1 3 -1 -1 2 1 1 -1 0 -1 0 0 -1 0 -1 0 1 1 0 0 0 1
0 0 0 1 0 -1 0 1 -1 -1 2 -1 1 0 -1 -1 -1 1 0 0 -1 1 1 -1 1 0 0 -2 1 1 0 0
-2 1 1 0 -1 2 -1 -2 2 1 0 2 0 0 1 -1 -1 0 0 -1 0 0 0 0 -1 0 1 0 -1 1 0 0
-2 0 1 -1 0 2 0 1 -1 0 -1 0 0 -1 0 1 1 1 0 1 0 0 -1 0 -1 0 -1 1 -1 0 0 1
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-2 1 1 0 1 2 -1 1 0 0 0 1 0 0 0 -1 -1 1 1 0 0 0 -1 0 0 0 -1 0 -1 0 -1 0
1 1 0 0 0 0 1 1 -1 2 -1 -1 1 0 -1 -1 0 0 0 0 0 -1 -1 0 0 0 0 1 -1 0 0 -1
-1 0 1 0 0 1 0 0 0 1 1 0 1 0 -1 -1 -1 0 -1 0 0 0 0 -1 0 0 1 -1 0 1 0 0
-3 1 1 -1 0 3 -2 -1 2 0 -1 3 -1 0 2 0 0 0 1 -1 0 -1 -1 1 -1 1 0 1 -1 0 -1 0
-1 1 1 0 0 1 0 0 0 1 -1 1 0 -1 0 0 0 0 0 0 0 0 -1 0 -1 0 0 1 -1 0 0 0
1 -2 -2 0 -1 -1 0 -2 2 -3 3 0 -1 0 1 1 0 0 0 0 -1 2 2 -1 1 0 1 -2 3 1 0 1
-1 -1 0 -2 0 2 0 -1 1 0 -1 1 -1 -1 1 2 2 0 0 0 0 0 -1 0 -1 0 0 2 0 0 0 1
-1 -1 0 -1 0 1 -1 0 1 -1 0 1 -1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 -1 0
-1 0 0 0 1 1 -1 2 -1 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 -1 0 0 0 -1 0
-1-1 0-1 0 1-1 0-1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0
-2 -1 0 -1 0 2 -1 -1 1 -1 0 1 -1 -1 1 2 1 0 0 0 0 1 0 0 -1 0 1 0 1 0 0 1
0 0 0 0 0 0 0 1 -1 1 0 -1 1 0 -1 0 0 0 -1 0 0 0 0 -1 0 0 1 0 0 1 0 0
2 -1 -1 1 0 -2 1 2 -2 -1 1 -3 1 0 -1 0 0 1 0 1 -1 1 1 -1 1 0 -1 -1 1 1 0 0
0 -1 -1 -1 0 1 0 -1 1 -1 0 0 -1 -1 1 2 1 0 0 0 0 1 0 0 -1 0 0 1 1 0 0 1
0 0 0 -1 0 1 0 0 0 0 -1 0 0 0 0 1 1 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0
0 0 0 -1 0 0 0 0 0 -1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
-1 -1 0 -2 0 2 0 0 0 0 -1 0 0 -1 0 2 2 0 0 1 0 0 -1 0 -1 0 0 1 0 0 0 1
-1 0 0-1 0 2 0 0 1-1 0 0-1 0 1 1 0 1 0 0-1 0-1 0 1-1 0 0 0
0 -1 -1 1 0 -1 0 0 0 -2 2 -1 0 0 0 0 -1 1 0 0 -1 2 1 -1 1 0 0 -2 2 1 0 1
32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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1 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 1 -1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 1 -1 1 2 -2 0 0 -2 1 0 -1 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0
-1 0 1 0 0 1-1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 -1 0 0 0 -1 2 0 0 0 0 -1 -1 0 0 0 0 1 1 0 1 0 0 -2 1 0 0 0
1 -1 -1 0 0 -1 0 0 0 -2 1 -1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 -1 2 0 0 0
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0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 -1 -2 1 -1 0 0 2 -1 1 0 -1 -1 -1 0 -1 0 0 1 1 -1 1 0 1 -2 1 1 1 0
0 0 0 0 0 0 0 -1 1 0 0 1 -1 0 1 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0
-1 0 1 0-1 1-1-2 2 1 2 0 1-1-1-1-1-1-1 0 0-1 0 2 0 1 0 0 0 0 0
0 1 1 1 0 0 0 1 -1 2 0 0 1 0 -1 -2 -1 0 0 0 0 -1 0 0 0 0 0 0 -1 0 0 -1
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 -1 0 -1 0 1 -1 0 1 -1 0 1 -1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 -1 0 0
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2 -1 -1 1 -1 -2 1 0 -1 -1 2 -2 1 -1 -1 0 0 1 0 1 -1 2 1 -2 1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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1 0 0 0 0 -1 1 1 -1 1 0 -1 1 0 -1 0 0 0 -1 0 0 0 0 -1 0 0 0 0 0 0 1 0
3 -1 -1 1 0 -3 2 2 -3 0 1 -4 2 0 -2 0 0 1 -1 1 -1 1 1 -1 1 0 -1 -1 1 1 1 0
-1 -2 -1 -1 -1 1 -1 -3 3 -3 2 2 -2 -1 2 2 1 0 0 0 0 2 1 0 0 0 1 -1 2 0 0 2
32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0-1 0-1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 1 -1 1 2 -2 0 0 -2 1 0 -1 0 0 1 0 1 0 0 0 0 0 0 -2 0 0 0 0 0
2 -2 -2 1 0 -2 1 0 -1 -4 2 -2 -1 -1 0 2 1 2 1 1 -1 3 1 -1 1 -1 -1 -1 2 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
3 0 -1 1 1 -2 2 2 -3 0 0 -3 1 0 -2 0 0 1 0 1 0 0 0 -1 1 -1 -1 0 0 0 0 0
0 0 0 -1 0 1 0 0 0 0 -1 0 0 0 0 1 1 0 0 0 0 0 -1 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0-1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0-1 1 0 0 0
-1 -1 0 -1 0 1 -1 0 1 -1 0 1 -1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 -1 0
1 -1 -1 0 0 -1 0 0 0 -2 1 -1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 -1 2 0 0 0
5 0 -2 3 0 -5 3 2 -4 -1 2 -5 2 0 -3 -1 -1 2 0 1 -1 2 1 -2 2 -1 -1 -2 1 1 1 0
1 0 0 0 0 -1 1 2 -2 0 0 -2 1 0 -1 0 0 1 0 1 0 0 0 0 0 0 -1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
-2 -1 0 -1 0 2 -1 -2 2 -2 0 2 -2 -1 2 2 1 0 0 0 0 1 0 0 -1 0 0 1 1 0 0 2
-1 0 0 0 0 1 -1 0 1 -1 0 2 -1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 0
2 -1 -1 1 0 -2 1 2 -2 -1 1 -2 1 0 -1 0 0 1 0 1 -1 1 1 -1 1 0 -1 -1 1 0 0 0
1 -1 -1 1 0 -2 0 0 0 -3 2 -1 -1 0 0 1 0 1 0 0 0 2 1 0 1 0 0 -2 2 0 0 1
32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 1 -1 1 2 -2 0 0 -2 1 0 -1 0 0 1 0 1 0 0 0 0 0 0 -2 0 0 0 0 0
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0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0-1 0-1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 -1 2 -1 -4 3 1 -3 0 1 -4 2 0 -2 -1 0 1 0 1 -1 1 1 -1 1 -1 -1 -1 0 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
3 0 -1 2 -1 -3 2 -1 -1 0 2 -2 1 0 -1 -1 -1 0 -1 0 0 1 1 -1 1 -1 1 -2 1 1 1 0
0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 1 0 0 0
0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 0 0 0
-1 -1 0 -1 0 1 -1 0 1 -1 0 1 -1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 -1 0
1 -1 -1 0 0 -1 0 0 0 -2 1 -1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 -1 2 0 0 0
2 0 -1 1 -1 -2 1 -1 0 -1 1 -1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 1 0 1 0
1 0 0 0 0 -1 1 2 -2 0 0 -2 1 0 -1 0 0 1 0 1 0 0 0 0 0 0 -1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
-1 1 1 0 0 1 0 0 0 1 -1 1 0 0 0 -1 0 0 0 0 0 -1 -1 0 0 0 0 1 -1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
3 -1 -1 1 0 -3 2 2 -3 0 1 -4 2 0 -2 0 0 1 -1 1 -1 1 1 -1 1 0 -1 -1 1 1 1 0
1 -1 -1 0 -1 -1 0 -1 1 -2 1 0 -1 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1
-
属性
积分=1
模块化=15
-
参考文献
G.Nebe,有限四元数矩阵群,
表征理论2,106-223(1998年4月)
-
笔记
强模格
-
URL(指向此晶格的其他站点的链接)
所有四元数矩阵群
-
最后一行
Haftungsausschluss/免责声明
加布里埃尔·内布