Applying Robert Boltje's theory of canonical induction, we give a restriction-preserving formula expressing any p-permutation module as a -linear combination of modules induced and inflated from projective modules associated with subquotient groups. The underlying constructions include, for any given finite group, a ring with a -basis indexed by conjugacy classes of triples where U is a subgroup, K is a -residue-free normal subgroup of U, and E is an indecomposable projective module of the group algebra of .
En application de la théorie de l'induction canonique de Robert Boltje, nous présentons une formule stable par restriction au moyen de laquelle tout module de p-permutation est exprimé sous forme de combinaison -linéaire des inductions des inflations des modules projectifs associés à des groupes de sous-quotients. Les constructions concernées comprennent, pour tout groupe fini, un anneau qui a une -base indexée par les classes de conjugaison des triplets avec U un sous-groupe, et E un module projectif indécomposable de l'algèbre de groupe de .
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@article{CRMATH_2019__357_4_327_0, author = {Barker, Laurence and Mutlu, Hatice}, title = {A new canonical induction formula for \protect\emph{p}-permutation modules}, journal = {Comptes Rendus. Math\'ematique}, pages = {327--332}, publisher = {Elsevier}, volume = {357}, number = {4}, year = {2019}, doi = {10.1016/j.crma.2019.04.004}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2019.04.004/} }
TY - JOUR AU - Barker, Laurence AU - Mutlu, Hatice TI - A new canonical induction formula for p-permutation modules JO - Comptes Rendus. Mathématique PY - 2019 SP - 327 EP - 332 VL - 357 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2019.04.004/ DO - 10.1016/j.crma.2019.04.004 LA - en ID - CRMATH_2019__357_4_327_0 ER -
%0 Journal Article %A Barker, Laurence %A Mutlu, Hatice %T A new canonical induction formula for p-permutation modules %J Comptes Rendus. Mathématique %D 2019 %P 327-332 %V 357 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2019.04.004/ %R 10.1016/j.crma.2019.04.004 %G en %F CRMATH_2019__357_4_327_0
Barker, Laurence; Mutlu, Hatice. A new canonical induction formula for p-permutation modules. Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 327-332. doi : 10.1016/j.crma.2019.04.004. http://archive.numdam.org/articles/10.1016/j.crma.2019.04.004/
[1] An inversion formula for the primitive idempotents of the trivial source algebra, J. Pure Appl. Math. (2019) (in press) | DOI
[2] A general theory of canonical induction formulae, J. Algebra, Volume 206 (1998), pp. 293-343
[3] Linear source modules and trivial source modules, Proc. Symp. Pure Math., Volume 63 (1998), pp. 7-30
[4] R. Boltje, Representation rings of finite groups, their species and idempotent formulae, preprint.
[5] The and constructions for biset functors, J. Algebra, Volume 523 (2019), pp. 241-273
[6] The primitive idempotents of the p-permutation ring, J. Algebra, Volume 323 (2010), pp. 2905-2915
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