In the Reflection Equation (RE) algebra associated with an involutive or Hecke symmetry $R$ the center is generated by elements ${\rm Tr}_R L^k$ (called the quantum power sums) , where $L$ is the generating matrix of this algebra and ${\rm Tr}_R$ is the $R$-trace corresponding to $R$. We consider the problem: whether it is so in RE-type algebras depending on spectral parameters. Mainly, we deal with algebras similar to those considered in [RS] (we call them the algebras of RS type). These algebras are defined by means of some current $R$-matrices arising from involutive and Hecke symmetries via the so-called Baxterization procedure. We define quantum power sums in the algebras of RS type and show that the lowest quantum power sum in such an algebra is central iff the value of the "charge" entering its definition is critical. Besides, we show that it is also so for higher quantum power sums under a complementary condition on the initial symmetry $R$.

中文翻译：

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广义反射方程代数的中心

在与对合或 Hecke 对称 $R$ 相关的反射方程 (RE) 代数中，中心由元素 ${\rm Tr}_R L^k$（称为量子功率和）生成，其中 $L$ 是生成这个代数的矩阵和 ${\rm Tr}_R$ 是对应于 $R$ 的 $R$-trace。我们考虑的问题是：在依赖谱参数的 RE 型代数中是否如此。我们主要处理类似于 [RS] 中考虑的代数（我们称它们为 RS 类型的代数）。这些代数是通过所谓的 Baxterization 过程通过对合对称性和 Hecke 对称性产生的一些当前 $R$-矩阵来定义的。我们在 RS 类型的代数中定义了量子功率和，并表明如果进入其定义的“电荷”值至关重要，则此类代数中的最低量子功率和是核心。除了，