乘法不变量与半群代数
Multiplicative Invariants and Semigroup Algebras
摘要：
设G是一个有限群，它通过自同构作用在格A上，从而作用在群代数S=k[A]上. S中的G-不变量的代数称为乘性不变量的代数。研究了乘法不变量代数是半群代数的条件。特别是，我们提出了一个明确的版本的结果法卡斯指出，乘法不变量的有限反射群确实是半群代数。另一方面，由不动点自由作用产生的乘法不变量被证明是半群代数。特别地，当G具有奇素数阶时，这成立。
英文摘要：
Let G be a finite group acting by automorphism on a lattice A, and hence on the group algebra S=k[A]. The algebra of G-invariants in S is called an algebra of multiplicative invariants. We investigate when algebras of multiplicative invariants are semigroup algebras. In particular, we present an explicit version of a result of Farkas stating that multiplicative invariants of finite reflection groups are indeed semigroup algebras. On the other hand, multiplicative invariants arising from fixed point free actions are shown to never be semigroup algebras. In particular, this holds whenever G has odd prime order.
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。
