Monomial G-posets and their Lefschetz invariants

JOURNAL OF ALGEBRA

卷:527

Article

Bouc, Serge¹  Mutlu, Hatice² 

[1] Univ Picardie Jules Verne, CNRS LAMFA, 33 Rue St Leu, F-80039 Amiens, France

[2] Bilkent Univ, Dept Math, TR-06800 Ankara, Turkey

关键词: Burnside ring;    Monomial;    Tensor induction;    Lefschetz invariant;   

DOI  :  10.1016/j.jalgebra.2019.02.036

来源: Elsevier

【 摘 要 】

Let G be a finite group, and C be an abelian group. We introduce the notions of C-monomial G-sets and C-monomial G-posets, and state some of their categorical properties. This gives in particular a new description of the C-monomial Burnside ring B-C(G). We also introduce Lefschetz invariants of C-monomial G-posets, which are elements of B-C(G). These invariants allow for a definition of a generalized tensor induction multiplicative map tau(U,lambda) BC (G) -> B-C(H) associated to any C-monomial (G, H)-biset (U, lambda), which in turn gives a group homomorphism B-C(G)(x) -> B-C(H)(x) between the unit groups of C-monomial Burnside rings. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free