| Linear Operators Preserving Symplectic Group over a Field Consisting of at Least Four Elements |
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| 作者姓名： | 游宏 刘绍武 |
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| 作者单位： | Department of Mathematics Harbin Institute of Technology Harbin，150001，Department of Mathematics Harbin Institute of Technology，Harbin，150001 School of Mathematical Science，Heilongjiang University，Harbin，150080 |
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| 基金项目： | The NSF (10571033) of China. |
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| 摘 要： | Suppose F is a field consisting of at least four elements. Let Mn(F) and SP2n(F) be the linear space of all n×n matrices and the group of all 2n×2n symplectic matrices over F, respectively. A linear operator L:M2n(F)→M2n(F) is said to preserve the symplectic group if L(SP2n(F))=SP2n(F). It is shown that L is an invertible preserver of the symplectic group if and only if L takes the form (i) L(X)=QPXP-1 for any X∈M2n(F) or (ii) L(X)=QPXTP-1 for any X∈M2n(F), where Q∈SP2n(F) and P is a generalized symplectic matrix. This generalizes the result derived by Pierce in Canad J. Math., 3(1975), 715-724.
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| 关 键 词： | 线性保护 偶对群 偶对矩阵 线性算子 |
Linear Operators Preserving Symplectic Group over a Field Consisting of at Least Four Elements |
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| YOU Hong LIU Shao-wu.Linear Operators Preserving Symplectic Group over a Field Consisting of at Least Four Elements[J].Northeastern Mathematical Journal,2006,22(2):219-232. |
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| Authors: | YOU Hong LIU Shao-wu |
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| Institution: | [1]Department of Mathematics, Harbin Institute of Technology, Harbin, 150001 [2]School of Mathematical Science, Heilongjiang University, Harbin, 150080 |
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| Abstract: | |
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| Keywords: | linear preserver symplectic group symplectic matrix generalized symplectic matrix linear operator |
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