Two-dimensional vector invariant rings of Abelian p-groups

✍ Scribed by Jianjun Chuai

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 123 KB
• Volume: 266
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00351-x

✦ Synopsis

For any faithful representation V of a non-trivial p-group over a field of characteristic p > 0, it is known that the ring of vector invariants of m copies of V is not Cohen-Macaulay if m 3. However, much less is known about the case m = 2. In this paper we show that, if m = 2 and the group is an Abelian p-group, then the ring of invariants of 2V is a complete intersection in some cases and is not Cohen-Macaulay in most cases. As a corollary we obtain that if the field is F p and the ring of invariants of the representation V is a polynomial ring, then the ring of invariants of 2V is either a complete intersection or not Cohen-Macaulay.