单项代数的平凡扩展是称性分数布劳尔配置代数
Trivial extensions of monomial algebras are symmetric fractional Brauer configuration algebras
AI总结：
本文通过等价定义建立了单项代数与分数布劳尔配置代数的关系，证明了其与平凡扩展的同构性，并建立了单项代数与称性分数布劳尔配置代数的对应关系。
摘要：
通过在某些特殊情况下提供分数布劳尔配置代数的等价定义，我们将每个单项代数与称为分数布劳尔配置的组合数据相关联，从而构造出相应的分数布劳尔配置代数。我们证明该代数与给定的单项代数的平凡扩展同构。此外，我们建立了单项代数的同构类与由类型S的称性分数布劳尔配置代数及其自由分数度函数的可约切割构成的等价类之间的一一对应关系。
英文摘要：
By providing equivalent definitions of fractional Brauer configuration algebras in certain special cases, we associate to each monomial algebra some combinatorial data called a fractional Brauer configuration, from which we construct a corresponding fractional Brauer configuration algebra. We show that this algebra is isomorphic to the trivial extension of the given monomial algebra. Furthermore, we establish a one-to-one correspondence between the isomorphism classes of monomial algebras and the equivalence classes of pairs consisting of a symmetric fractional Brauer configuration algebra of type S with a free fractional-degree function and an admissible cut on it.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
