Institute for Mathematical Physics Gauss Decompositions for Quantum Groups and Supergroups in Memory of Victor Nikolaevich Popov Gauss Decomposition for Quantum Groups and Supergroups
Institute for Mathematical Physics Gauss Decompositions for Quantum Groups and Supergroups in Memory of Victor Nikolaevich Popov Gauss Decomposition for Quantum Groups and Supergroups
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数学物理研究所 纪念维克多·尼古拉耶维奇·波波夫 量子群和超群的高斯分解 量子群和超群的高斯分解
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通讯作者：
M. A. Sokolov
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作者：
E. Damaskinsky;P. Kulish;M. A. Sokolov
用初等代数方法和r -矩阵方法研究了与经典李群和超群相关的量子群的高斯分解。详细描述了由分解引入的新基发生器之间的交换关系。结果表明，将新基中的独立生成子数约简为相关经典（超）群的维数是可能的。在变形情况下，不改变高斯分解生成的（超）行列式的经典表达式。以辛量子群Sp q(2)和超群GL q（1|1）、GL q（2|1）为例。
The Gauss decompositions of the quantum groups, related to classical Lie groups and su-pergroups are considered by the elementary algebraic and R-matrix methods. The commu-tation relations between new basis generators (which are introduced by the decomposition) are described in some details. It is shown that the reduction of the independent generator number in the new basis to the dimension of related classical (super) group is possible. The classical expression for (super) determinant through the Gauss decomposition generators is not changed in the deformed case. The symplectic quantum group Sp q (2) and supergroups GL q (1|1), GL q (2|1) are considered as examples.