标题： 逆独异元拓扑量子场论和开-闭大 canonical 对称轨道模型 显示英文标题

标题： Inverse Monoid Topological Quantum Field Theories and Open-Closed Grand Canonical Symmetric Orbifolds

摘要： 我们提出一种针对逆独异的开-闭拓扑量子场论，该理论推广了在带边界的黎曼曲面上具有有限规范群的主纤维丛理论。 该理论是通过半单逆独异代数与矩阵代数之间的同构构建的，这体现了独异结构和表示理论的核心内容。 我们详细研究的一个例子是部分排列的Ivanov-Kerov独异。 我们回顾了来自弦理论的动机，以解释带有边界的覆盖的广义规范理论。 显示英文摘要

摘要： We present an open-closed topological quantum field theory for inverse monoids which generalizes the theory of principle fiber bundles with finite gauge group over Riemann surfaces with boundary. The theory is constructed using the isomorphism between the semisimple inverse monoid algebra and a matrix algebra which lies at the heart of monoid structure and representation theory. An example that we study in detail is the Ivanov-Kerov monoid of partial permutations. We review motivations from string theory for the resulting grand canonical theory of covers with boundaries.