Berezinians, Exterior Powers and Recurrent Sequences
Berezinians, Exterior Powers and Recurrent Sequences
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Berezinians、外力和循环序列
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
T. Voronov
中科院分区：
文献类型：
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作者：
H. Khudaverdian;T. Voronov
本文研究了线性算子A的特征函数在p中的幂展开式|我们证明了A的外幂的迹满足周期为q的普适递归关系。“底层”递归关系在GL（V）的表示的Grothendieck环中成立。它们通过在这个环中q+1阶的某些汉克尔行列式的消失来表示，这推广了普通向量空间的足够高的外幂的消失。特别地，这允许将算子的Berezian表示为两个多项式不变量的比率。我们分析了超空间中的Cayley-Hamilton恒等式。利用Berezinian的几何意义，我们也给出了类似Cramer规则的一个简单公式
We study power expansions of the characteristic function of a linear operator A in a p|q-dimensional superspace V. We show that traces of exterior powers of A satisfy universal recurrence relations of period q. ‘Underlying’ recurrence relations hold in the Grothendieck ring of representations of GL(V). They are expressed by vanishing of certain Hankel determinants of order q+1 in this ring, which generalizes the vanishing of sufficiently high exterior powers of an ordinary vector space. In particular, this allows to express the Berezinian of an operator as a ratio of two polynomial invariants. We analyze the Cayley–Hamilton identity in a superspace. Using the geometric meaning of the Berezinian we also give a simple formulation of the analog of Cramer’s rule