标题： $C^*$-费米系统和详细平衡 显示英文标题

标题： $C^*$-fermi systems and detailed balance

摘要： 关于张量积的$\mathbb Z_2$-分次$*$-代数以及$\mathbb Z_2$-分次$C^*$-代数的产品和对角态，建立了一个系统的理论。 作为实现这一目标的初步步骤，我们提供了$\mathbb Z_2$-分次$C^*$-代数的{\it 任意子$C^*$-张量乘积}的构造。 随后研究了冯诺依曼代数之间正线性映射的扭曲对偶，并将其应用于解决无限费米格子上的正性问题。 最后，这些结果用于在具有类型$\mathbb Z_2$分级的一般$C^*$系统中定义费米子详细平衡（该定义包括通常张量积的特殊情况），通过将此类系统视为复合系统的一部分，并利用对角态。 显示英文摘要

摘要： A systematic theory of product and diagonal states is developed for tensor products of $\mathbb Z_2$-graded $*$-algebras, as well as $\mathbb Z_2$-graded $C^*$-algebras. As a preliminary step to achieve this goal, we provide the construction of a {\it fermionic $C^*$-tensor product} of $\mathbb Z_2$-graded $C^*$-algebras. Twisted duals of positive linear maps between von Neumann algebras are then studied, and applied to solve a positivity problem on the infinite Fermi lattice. Lastly, these results are used to define fermionic detailed balance (which includes the definition for the usual tensor product as a particular case) in general $C^*$-systems with gradation of type $\mathbb Z_2$, by viewing such a system as part of a compound system and making use of a diagonal state.