We define a notion of depth for an inclusion of complex semisimple
algebras, based on a comparison of powers of the induction-restriction table
(and its transpose matrix) and a previous notion of depth in an earlier paper
of the second author. We prove that a depth two extension of complex
semisimple algebras is normal in the sense of Rieffel, and conversely. Given
an extension H ⊆ G of finite groups we prove that the depth of C H in C G is
bounded by 2n if the kernel of the permutation representation of G on cosets
of H is the intersection of n conjugate subgroups of H. We prove in several
ways that the subgroup depth of symmetric groups Sn ⊆ Sn+1 is 2n − 1. An
appendix by S. Danz and B. K¨ulshammer determines the subgroup depth of
alternating groups An ⊆ An+1 and dihedral group extensions.
ring extension depth group algebra Hopf algebra normal subring inclusion matrix
Diğer ID | JA97UD42EE |
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Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 1 Haziran 2011 |
Yayımlandığı Sayı | Yıl 2011 Cilt: 9 Sayı: 9 |