Clifford theory for Mackey algebras

Yaraneri E.

JOURNAL OF ALGEBRA, cilt.303, sa.1, ss.244-274, 2006 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 303 Sayı: 1
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1016/j.jalgebra.2006.01.049
  • Dergi Adı: JOURNAL OF ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.244-274
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

We develop a Clifford theory for Mackey algebras. For simple Mackey functors, using their classification we prove Mackey algebra versions of Clifford's theorem and the Clifford correspondence. Let mu(R)(G) be the Mackey algebra of a finite group G over a commutative unital ring R, and let 1(N) be the unity of mu(R)(N) where N is a normal subgroup of G. Observing that 1(N)mu(R)(G)1(N) is a crossed product of G/N over mu R(N), a number of results concerning group graded algebras are extended to the context of Mackey algebras, including Fong's theorem, Green's indecomposibility theorem and some reduction and extension techniques for indecomposable Mackey functors. (c) 2006 Elsevier Inc. All rights reserved.