群代数 kA ₄ 的表示环的 Z ₊-模分类

Classification of Z ₊-modules over the representation ring of group algebra kA ₄

摘要

设 k 是代数闭域,且 char(k)≠12,记 r(kA ₄)为群代数 kA ₄ 的表示环,本文对 r(kA ₄)上所有的不可约 Z ₊-模分类,证明在等价意义下共有 9 个不可约 Z ₊-模。

Abstract

Let k be an algebraically closed field with char(k)≠12, denoted r(kA ₄) the representation ring of group algebra r(kA ₄). All irreducible Z ₊-modules over r(kA ₄) are classified. We prove that there are 9 non-equivalent irreducible Z ₊-modules.

关键词

群代数 kA ₄ / 不可约 Z ₊-模 / 表示环 / 矩阵方程

Key words

group algebra kA ₄ / irreducible Z ₊-module / representation ring / matrix equation

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基金资助

国家自然科学基金资助项目(12201545)