In the present paper we develop the algebraic Bethe ansatz approach to the case of non-skew-symmetric $gl(2)\otimes gl(2)$-valued Cartan-non-invariant classical r-matrices with spectral parameters. We consider the two families of these r-matrices, namely, the two non-standard rational r-matrices twisted with the help of second order automorphisms and realize the algebraic Bethe ansatz method for them. We study physically important examples of the Gaudin-type and BCS-type systems associated with these r-matrices and obtain explicitly the Bethe vectors and the spectrum for the corresponding quantum hamiltonians in terms of solutions of Bethe equations.

在本文中，我们针对非偏对称情况开发了代数Bethe ansatz方法 $G升（\mathrm{2个}）\otimes G升（\mathrm{2个}）$谱参数的超值Cartan非不变经典r-矩阵。我们考虑了这些r矩阵的两个族，即在二阶自同构的帮助下扭曲的两个非标准有理r矩阵，并为它们实现了代数Bethe ansatz方法。我们研究了与这些r矩阵相关的Gaudin型和BCS型系统的重要物理实例，并根据Bethe方程的解明确获得了Bethe向量和相应的量子哈密顿量的光谱。