On $p$-permutation equivalences between direct products of blocks

Deniz Yılmaz

doi:10.15672/hujms.1439414

Araştırma Makalesi

On $p$-permutation equivalences between direct products of blocks

Yıl 2025, Cilt: 54 Sayı: 3, 869 - 873, 24.06.2025

Deniz Yılmaz

https://doi.org/10.15672/hujms.1439414

Öz

We extend the notion of a $p$-permutation equivalence to an equivalence between direct products of block algebras. We prove that a $p$-permutation equivalence between direct products of blocks gives a bijection between the factors and induces a $p$-permutation equivalence between corresponding blocks.

Anahtar Kelimeler

block, p-permutation equivalence, trivial source modules

Kaynakça

[1] R. Boltje and P. Perepelitsky, p-permutation equialences between blocks of group algebras, arXiv:2007.09253.
[2] R. Boltje and B. Xu, On p-permutation equivalences: Between Rickard equivalences and isotypies, Trans. Amer. Math. Soc. 360, 5067-5087, 2008.
[3] S. Bouc and D. Yılmaz, Diagonal p-permutation functors, semisimplicity, and functorial equivalence of blocks, Adv. Math. 411, 108799, 2022.
[4] M. Broué, Isométries parfaites, types de blocs, catégories dérivées, Astérisque 181(182), 61-92, 1990.
[5] J. Rickard, Splendid equivalences: derived categories and permutation modules, Proc. London Math. Soc. 72, 331-358, 1996.
[6] L. Puig, On the local structure of Morita and Rickard equivalences between Brauer blocks, Progress in Mathematics, 178, Birkhäuser Verlag, Basel, 1999.

Yıl 2025, Cilt: 54 Sayı: 3, 869 - 873, 24.06.2025

Deniz Yılmaz

https://doi.org/10.15672/hujms.1439414

Öz

Kaynakça

[1] R. Boltje and P. Perepelitsky, p-permutation equialences between blocks of group algebras, arXiv:2007.09253.
[2] R. Boltje and B. Xu, On p-permutation equivalences: Between Rickard equivalences and isotypies, Trans. Amer. Math. Soc. 360, 5067-5087, 2008.
[3] S. Bouc and D. Yılmaz, Diagonal p-permutation functors, semisimplicity, and functorial equivalence of blocks, Adv. Math. 411, 108799, 2022.
[4] M. Broué, Isométries parfaites, types de blocs, catégories dérivées, Astérisque 181(182), 61-92, 1990.
[5] J. Rickard, Splendid equivalences: derived categories and permutation modules, Proc. London Math. Soc. 72, 331-358, 1996.
[6] L. Puig, On the local structure of Morita and Rickard equivalences between Brauer blocks, Progress in Mathematics, 178, Birkhäuser Verlag, Basel, 1999.

Toplam 6 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Grup Teorisi ve Genellemeler
Bölüm	Matematik
Yazarlar	Deniz Yılmaz 0000-0002-4245-8154
Erken Görünüm Tarihi	27 Ağustos 2024
Yayımlanma Tarihi	24 Haziran 2025
Gönderilme Tarihi	19 Şubat 2024
Kabul Tarihi	14 Temmuz 2024
Yayımlandığı Sayı	Yıl 2025 Cilt: 54 Sayı: 3

Kaynak Göster

APA	Yılmaz, D. (2025). On $p$-permutation equivalences between direct products of blocks. Hacettepe Journal of Mathematics and Statistics, 54(3), 869-873. https://doi.org/10.15672/hujms.1439414
AMA	Yılmaz D. On $p$-permutation equivalences between direct products of blocks. Hacettepe Journal of Mathematics and Statistics. Haziran 2025;54(3):869-873. doi:10.15672/hujms.1439414
Chicago	Yılmaz, Deniz. “On $p$-Permutation Equivalences Between Direct Products of Blocks”. Hacettepe Journal of Mathematics and Statistics 54, sy. 3 (Haziran 2025): 869-73. https://doi.org/10.15672/hujms.1439414.
EndNote	Yılmaz D (01 Haziran 2025) On $p$-permutation equivalences between direct products of blocks. Hacettepe Journal of Mathematics and Statistics 54 3 869–873.
IEEE	D. Yılmaz, “On $p$-permutation equivalences between direct products of blocks”, Hacettepe Journal of Mathematics and Statistics, c. 54, sy. 3, ss. 869–873, 2025, doi: 10.15672/hujms.1439414.
ISNAD	Yılmaz, Deniz. “On $p$-Permutation Equivalences Between Direct Products of Blocks”. Hacettepe Journal of Mathematics and Statistics 54/3 (Haziran 2025), 869-873. https://doi.org/10.15672/hujms.1439414.
JAMA	Yılmaz D. On $p$-permutation equivalences between direct products of blocks. Hacettepe Journal of Mathematics and Statistics. 2025;54:869–873.
MLA	Yılmaz, Deniz. “On $p$-Permutation Equivalences Between Direct Products of Blocks”. Hacettepe Journal of Mathematics and Statistics, c. 54, sy. 3, 2025, ss. 869-73, doi:10.15672/hujms.1439414.
Vancouver	Yılmaz D. On $p$-permutation equivalences between direct products of blocks. Hacettepe Journal of Mathematics and Statistics. 2025;54(3):869-73.