Crossed Burnside Rings I. The Fundamental Theorem

✍ Scribed by Fumihito Oda; Tomoyuki Yoshida

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 283 KB
• Volume: 236
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8341

✦ Synopsis

Let G be a finite group and S a finite G-monoid. A crossed G-set over S is a finite G-set equipped with a G-map into S called a weight function. A crossed Ž . Burnside ring X ⍀ G, S is the Grothendieck ring of the category of crossed G-sets with respect to disjoint unions and tensor products. In this paper, we prove the fundamental theorem of crossed Burnside rings and an idempotent formula at characteristic 0. ᮊ 2001 Academic Press CONTENTS 1. Introduction. 1.1. Operations compatible with inductions and restrictions. 1.2. Crossed G-sets. 1.3. Main results. 1.4. Notation. 1 Ž .