Faith猜测与余环的同调理论
基本信息
结项摘要
1939年Nakayama在研究Frobenius代数时引入了QF环的概念。此后，QF环吸引了众多代数学家的兴趣，尤其是环论和Hopf代数专家的兴趣，他们从不同角度给出了QF环的刻画，并围绕QF环提出了众多问题，其中最为著名的是Faith提出的三大猜测(FGF猜测，Faith-Menal猜测，Faith猜测)以及Nicholson和Yousif提出的21个具有挑战性的问题（至今仍未解决）。QF环是域上有限群的群代数的推广，而群代数是一种典型的Hopf代数。因此自然而然地提出了QCF余代数的概念。本项目拟围绕Faith三大猜测给出QF环新的性质刻画，推进猜测研究进程，回答Nicholson与Yousif的部分问题。同时刻划QCF余环，并用挠理论与余挠理论研究余环的同调性质，作为应用，将给出著名的Drinfel'd量子偶新的结构性质，进一步讨论物理场上量子杨-Baxter方程解的代数特性。
项目摘要
项目成果
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数据更新时间：2023-05-31
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