非分裂域情形下的Cartan不变量与Ikeda定理

Cartan Invariants under Non-Splitting Field and IKEDA Theorem

在有限群的模表示理论中,通常涉及到Cartan不变量时,往往要求基域为分裂域。本文讨论了基域为非分裂域情形时Cartan不变量的形式及相关的几个命题,且利用它们证明了非分裂域情形下关于满的局部内G—代数的Ikeda定理。

In the modular representation theory of finite groups, when Cartan invariants are dealt with, the residue field is often assumed to be a splitting field. This paper discusses the forms of Cartan matrix in the case of non-splitting field and proves IKEDA theorem on epimorphic local interior G-algebras.