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

By results of Boltje and Kulshammer, if a source algebra A of a
Keywords:

Source algebra,

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  • 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.