Affiliation:
1. Department of Mathematics , City, University of London , London , United Kingdom
Abstract
Abstract
Let 𝐺 be one of the sporadic simple Mathieu groups
M
11
M_{11}
,
M
12
M_{12}
,
M
22
M_{22}
,
M
23
M_{23}
or
M
24
M_{24}
, and suppose 𝑘 is an algebraically closed field of prime characteristic 𝑝, dividing the order of 𝐺.
In this paper, we describe some of the Lie algebra structure of the first Hochschild cohomology groups of the 𝑝-blocks of
k
G
kG
.
In particular, we calculate the dimension of
HH
1
(
B
)
\mathrm{HH}^{1}(B)
for the 𝑝-blocks 𝐵 of
k
G
kG
, and in almost all cases, we determine whether
HH
1
(
B
)
\mathrm{HH}^{1}(B)
is a solvable Lie algebra.
Subject
Algebra and Number Theory
Reference45 articles.
1. J. B. An and M. Conder,
The Alperin and Dade conjectures for the simple Mathieu groups,
Comm. Algebra 23 (1995), no. 8, 2797–2823.
2. D. Benson, R. Kessar and M. Linckelmann,
On the BV structure of the Hochschild cohomology of finite group algebras,
Pacific J. Math. 313 (2021), no. 1, 1–44.
3. D. J. Benson,
Representations and Chomology. II: Cohomology of Groups and Modules,
Cambridge Stud. Adv. Math. 31,
Cambridge University, Cambridge, 1991.
4. D. J. Benson and J. F. Carlson,
Diagrammatic methods for modular representations and cohomology,
Comm. Algebra 15 (1987), no. 1–2, 53–121.
5. R. Brauer,
On the arithmetic in a group ring,
Proc. Natl. Acad. Sci. USA 30 (1944), 109–114.
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