The Brauer-Clifford group of G-rings

JOURNAL OF ALGEBRA

卷:341

Article

Turull, Alexandre

关键词: Clifford theory;    Brauer group;    Schur index;    Finite groups;    Representations;   

DOI  :  10.1016/j.jalgebra.2011.05.040

来源: Elsevier

【 摘 要 】

In previous work, the author introduced the Brauer-Clifford group of certain G-algebras. This group is useful because to every irreducible character of a normal subgroup of a finite group, one can associate a unique element of a specific Brauer-Clifford group, and this element controls the Clifford theory of this character in its ambient group. In the present paper, we define the Brauer-Clifford group of G-rings. This new definition only requires us to discuss tensor products over the underlying G-ring, and it is simpler than the earlier one. We prove that the new definition yields a group which is canonically isomorphic to the Brauer-Clifford group of a corresponding suitable G-algebra. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free