Details
| Original language | English |
|---|---|
| Pages (from-to) | 29-43 |
| Number of pages | 15 |
| Journal | Glasgow mathematical journal |
| Volume | 49 |
| Issue number | 1 |
| Publication status | Published - Jan 2007 |
| Externally published | Yes |
Abstract
Except for blocks with a cyclic or Klein four defect group, it is not known in general whether the Morita equivalence class of a block algebra over a field of prime characteristic determines that of the corresponding block algebra over a padic ring. We prove this to be the case when the defect group is quaternion of order 8 and the block algebra over an algebraically closed field k of characteristic 2 is Morita equivalent to kÃ4. The main ingredients are Erdmann's classification of tame blocks [6] and work of Cabanes and Picaronny [4, 5] on perfect isometrics between tame blocks.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Glasgow mathematical journal, Vol. 49, No. 1, 01.2007, p. 29-43.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Blocks with a quaternion defect group over a 2-adic ring
T2 - The case Ã4
AU - Holm, Thorsten
AU - Kessar, Radha
AU - Linckelmann, Markus
PY - 2007/1
Y1 - 2007/1
N2 - Except for blocks with a cyclic or Klein four defect group, it is not known in general whether the Morita equivalence class of a block algebra over a field of prime characteristic determines that of the corresponding block algebra over a padic ring. We prove this to be the case when the defect group is quaternion of order 8 and the block algebra over an algebraically closed field k of characteristic 2 is Morita equivalent to kÃ4. The main ingredients are Erdmann's classification of tame blocks [6] and work of Cabanes and Picaronny [4, 5] on perfect isometrics between tame blocks.
AB - Except for blocks with a cyclic or Klein four defect group, it is not known in general whether the Morita equivalence class of a block algebra over a field of prime characteristic determines that of the corresponding block algebra over a padic ring. We prove this to be the case when the defect group is quaternion of order 8 and the block algebra over an algebraically closed field k of characteristic 2 is Morita equivalent to kÃ4. The main ingredients are Erdmann's classification of tame blocks [6] and work of Cabanes and Picaronny [4, 5] on perfect isometrics between tame blocks.
UR - http://www.scopus.com/inward/record.url?scp=34248995875&partnerID=8YFLogxK
U2 - 10.1017/S0017089507003394
DO - 10.1017/S0017089507003394
M3 - Article
AN - SCOPUS:34248995875
VL - 49
SP - 29
EP - 43
JO - Glasgow mathematical journal
JF - Glasgow mathematical journal
SN - 0017-0895
IS - 1
ER -