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Search: MSC category 20C20 ( Modular representations and characters )

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1. CMB 2011 (vol 55 pp. 48)

Chebolu, Sunil K.; Christensen, J. Daniel; Mináč, Ján
Freyd's Generating Hypothesis for Groups with Periodic Cohomology
Let $G$ be a finite group, and let $k$ be a field whose characteristic $p$ divides the order of $G$. Freyd's generating hypothesis for the stable module category of $G$ is the statement that a map between finite-dimensional $kG$-modules in the thick subcategory generated by $k$ factors through a projective if the induced map on Tate cohomology is trivial. We show that if $G$ has periodic cohomology, then the generating hypothesis holds if and only if the Sylow $p$-subgroup of $G$ is $C_2$ or $C_3$. We also give some other conditions that are equivalent to the GH for groups with periodic cohomology.

Keywords:Tate cohomology, generating hypothesis, stable module category, ghost map, principal block, thick subcategory, periodic cohomology
Categories:20C20, 20J06, 55P42

2. CMB 2011 (vol 55 pp. 38)

Butske, William
Endomorphisms of Two Dimensional Jacobians and Related Finite Algebras
Zarhin proves that if $C$ is the curve $y^2=f(x)$ where $\textrm{Gal}_{\mathbb{Q}}(f(x))=S_n$ or $A_n$, then ${\textrm{End}}_{\overline{\mathbb{Q}}}(J)=\mathbb{Z}$. In seeking to examine his result in the genus $g=2$ case supposing other Galois groups, we calculate $\textrm{End}_{\overline{\mathbb{Q}}}(J)\otimes_{\mathbb{Z}} \mathbb{F}_2$ for a genus $2$ curve where $f(x)$ is irreducible. In particular, we show that unless the Galois group is $S_5$ or $A_5$, the Galois group does not determine ${\textrm{End}}_{\overline{\mathbb{Q}}}(J)$.

Categories:11G10, 20C20

3. CMB 2006 (vol 49 pp. 285)

Riedl, Jeffrey M.
Orbits and Stabilizers for Solvable Linear Groups
We extend a result of Noritzsch, which describes the orbit sizes in the action of a Frobenius group $G$ on a finite vector space $V$ under certain conditions, to a more general class of finite solvable groups $G$. This result has applications in computing irreducible character degrees of finite groups. Another application, proved here, is a result concerning the structure of certain groups with few complex irreducible character degrees.

Categories:20B99, 20C15, 20C20

4. CMB 2006 (vol 49 pp. 96)

Külshammer, Burkhard
Roots of Simple Modules
We introduce roots of indecomposable modules over group algebras of finite groups, and we investigate some of their properties. This allows us to correct an error in Landrock's book which has to do with roots of simple modules.

Categories:20C20, 20C05

5. CMB 2000 (vol 43 pp. 79)

König, Steffen
Cyclotomic Schur Algebras and Blocks of Cyclic Defect
An explicit classification is given of blocks of cyclic defect of cyclotomic Schur algebras and of cyclotomic Hecke algebras, over discrete valuation rings.

Categories:20G05, 20C20, 16G30, 17B37, 57M25

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