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首页> 外文期刊>Journal of algebra and its applications >AN ALGEBRAIC APPROACH TO SYMMETRIC PRE-MONOIDAL STATISTICS
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AN ALGEBRAIC APPROACH TO SYMMETRIC PRE-MONOIDAL STATISTICS

机译：对称前正态统计的一种代数方法

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摘要

Recently, generalized Bose–Fermi statistics was studied in a category theoretic framework and to accommodate this endeavor the notion of a pre-monoidal category was developed. Here we describe an algebraic approach for the construction of such categories. We introduce a procedure called twining which breaks the quasi-bialgebra structure of the universal enveloping algebras of semi-simple Lie algebras and renders the category of finite-dimensional modules pre-monoidal. The category is also symmetric, meaning that each object of the category provides representations of the symmetric groups, which allows for a generalized boson-fermion statistic to be defined. Exclusion and confinement principles for systems of indistinguishable particles are formulated as an invariance with respect to the actions of the symmetric group. We apply the procedure to suggest that the symmetries which can be associated to color, spin and flavor degrees of freedom lead to confinement of states.
机译：最近，在类别理论框架中研究了广义的Bose-Fermi统计量，并为适应这种努力，开发了前正弦类别的概念。在这里，我们描述了构建此类的代数方法。我们介绍了一种称为孪生的过程，该过程打破了半简单李代数的通用包络代数的准双代数结构，并使有限维模数的类别为先莫诺代数。该类别也是对称的，这意味着该类别的每个对象都提供了对称组的表示，这允许定义广义玻色子-费米子统计量。将不可区分粒子系统的排除和限制原理表述为关于对称基团作用的不变性。我们应用该程序表明可以与颜色，自旋和风味自由度相关的对称性导致状态的限制。

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