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 $R$. 查看全文>>