Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, , 68 - 72, 05.07.2018
https://doi.org/10.24330/ieja.440216

Öz

Kaynakça

  • R. Boltje and B. Kulshammer, On the depth 2 condition for group algebra and Hopf algebra extensions, J. Algebra, 323(6) (2010), 1783-1796.
  • R. Boltje and B. Kulshammer, Group algebra extensions of depth one, Algebra Number Theory, 5(1) (2011), 63-73.
  • C. W. Curtis and I. Reiner, Methods of Representation Theory, Vol. II, with applications to nite groups and orders, Pure and Applied Mathematics (New York), A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1987.
  • L. Kadison and K. Szlachanyi, Bialgebroid actions on depth two extensions, Adv. Math., 179(1) (2003), 75-121.
  • M. Linckelmann, On splendid derived and stable equivalences between blocks of nite groups, J. Algebra, 242(2) (2001), 819-843.
  • L. Puig, Nilpotent blocks and their source algebras, Invent. Math., 93(1) (1988), 77-116.
  • L. Puig, Pointed groups and construction of modules, J. Algebra, 116(1) (1988), 7-129.
  • [L. Puig, The hyperfocal subalgebra of a block, Invent. Math., 141(2) (2000), 365-397.
  • J.-P. Serre, Corps Locaux, Deuxieme edition, Publications de l'Universite de Nancago, No. VIII, Hermann, Paris, 1968.
  • J. Thevenaz, G-Algebras and Modular Representation Theory, Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995.
  • A. Watanabe, Note on hyperfocal subalgebras of blocks of nite groups, J. Algebra, 322(2) (2009), 449-452.

A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP

Yıl 2018, , 68 - 72, 05.07.2018
https://doi.org/10.24330/ieja.440216

Öz

By results of Boltje and Kulshammer, if a source algebra A of a
principal p-block of a nite group with a defect group P with inertial quotient
E is a depth two extension of the group algebra of P, then A is isomorphic
to a twisted group algebra of the group P o E. We show in this note that
this is true for arbitrary blocks. We observe further that the results of Boltje
and Kulshammer imply that A is a depth two extension of its hyperfocal
subalgebra, with a criterion for when this is a depth one extension. By a
result of Watanabe, this criterion is satised if the defect groups are abelian.

Kaynakça

  • R. Boltje and B. Kulshammer, On the depth 2 condition for group algebra and Hopf algebra extensions, J. Algebra, 323(6) (2010), 1783-1796.
  • R. Boltje and B. Kulshammer, Group algebra extensions of depth one, Algebra Number Theory, 5(1) (2011), 63-73.
  • C. W. Curtis and I. Reiner, Methods of Representation Theory, Vol. II, with applications to nite groups and orders, Pure and Applied Mathematics (New York), A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1987.
  • L. Kadison and K. Szlachanyi, Bialgebroid actions on depth two extensions, Adv. Math., 179(1) (2003), 75-121.
  • M. Linckelmann, On splendid derived and stable equivalences between blocks of nite groups, J. Algebra, 242(2) (2001), 819-843.
  • L. Puig, Nilpotent blocks and their source algebras, Invent. Math., 93(1) (1988), 77-116.
  • L. Puig, Pointed groups and construction of modules, J. Algebra, 116(1) (1988), 7-129.
  • [L. Puig, The hyperfocal subalgebra of a block, Invent. Math., 141(2) (2000), 365-397.
  • J.-P. Serre, Corps Locaux, Deuxieme edition, Publications de l'Universite de Nancago, No. VIII, Hermann, Paris, 1968.
  • J. Thevenaz, G-Algebras and Modular Representation Theory, Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995.
  • A. Watanabe, Note on hyperfocal subalgebras of blocks of nite groups, J. Algebra, 322(2) (2009), 449-452.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Markus Linckelmann Bu kişi benim

Yayımlanma Tarihi 5 Temmuz 2018
Yayımlandığı Sayı Yıl 2018

Kaynak Göster

APA Linckelmann, M. (2018). A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP. International Electronic Journal of Algebra, 24(24), 68-72. https://doi.org/10.24330/ieja.440216
AMA Linckelmann M. A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP. IEJA. Temmuz 2018;24(24):68-72. doi:10.24330/ieja.440216
Chicago Linckelmann, Markus. “A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP”. International Electronic Journal of Algebra 24, sy. 24 (Temmuz 2018): 68-72. https://doi.org/10.24330/ieja.440216.
EndNote Linckelmann M (01 Temmuz 2018) A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP. International Electronic Journal of Algebra 24 24 68–72.
IEEE M. Linckelmann, “A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP”, IEJA, c. 24, sy. 24, ss. 68–72, 2018, doi: 10.24330/ieja.440216.
ISNAD Linckelmann, Markus. “A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP”. International Electronic Journal of Algebra 24/24 (Temmuz 2018), 68-72. https://doi.org/10.24330/ieja.440216.
JAMA Linckelmann M. A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP. IEJA. 2018;24:68–72.
MLA Linckelmann, Markus. “A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP”. International Electronic Journal of Algebra, c. 24, sy. 24, 2018, ss. 68-72, doi:10.24330/ieja.440216.
Vancouver Linckelmann M. A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP. IEJA. 2018;24(24):68-72.