Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.01061 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914897669914624 |
|---|---|
| author | Schaps, Mary Zvi, Zehavit |
| author_facet | Schaps, Mary Zvi, Zehavit |
| contents | We consider the effect of performing an elementary equivalence as defined by Okuyama on a group block of form $F(C_p \times C_p)\rtimes C_r$, for a field $F$ of characteristic $p$. If $I=\{0,1,2,\dots r-1\}$ is the set of residues corresponding to the simple modules of $FC_r$, the elementary equivalence is determined by a proper, non-empty subset $I_0 \subset I$, and the corresponding elementary tilting complex is completely determined by $I_0$.
We give a catalog of homogeneous maps between irreducible components of the elementary tilting complex. When the subset $I_0$ is an interval, we prove that the maps in the catalog are sufficient to describe all homogeneous maps between two irreducible components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01061 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Elementary equivalences for blocks with normal elementary abelian defect group of rank 2 Schaps, Mary Zvi, Zehavit Representation Theory 20C20 (Primary) 20C05 (Secondary) We consider the effect of performing an elementary equivalence as defined by Okuyama on a group block of form $F(C_p \times C_p)\rtimes C_r$, for a field $F$ of characteristic $p$. If $I=\{0,1,2,\dots r-1\}$ is the set of residues corresponding to the simple modules of $FC_r$, the elementary equivalence is determined by a proper, non-empty subset $I_0 \subset I$, and the corresponding elementary tilting complex is completely determined by $I_0$. We give a catalog of homogeneous maps between irreducible components of the elementary tilting complex. When the subset $I_0$ is an interval, we prove that the maps in the catalog are sufficient to describe all homogeneous maps between two irreducible components. |
| title | Elementary equivalences for blocks with normal elementary abelian defect group of rank 2 |
| topic | Representation Theory 20C20 (Primary) 20C05 (Secondary) |
| url | https://arxiv.org/abs/2408.01061 |