On the Cartan matrix of Mackey algebras

Details On the Cartan matrix of Mackey algebras On the Cartan matrix of Mackey algebras

2010-01-02

arxiv.org/abs/1001.0321v2

Mathematics

Group Theory

Scientific paper

Let k be a field of characteristic p>0, and G be a finite group. The first result of this paper is an explicit formula for the determinant of the Cartan matrix of the Mackey algebra mu_k(G) of G over k. The second one is a formula for the rank of the Cartan matrix of the cohomological Mackey algebra comu_k(G) of G over k, and a characterization of the groups G for which this matrix is non singular. The third result is a generalization of this rank formula and characterization to blocks of comu_k(G) : in particular, if b is a block of kG, the Cartan matrix of the corresponding block comu_k(b) of comu_k(G) is non singular if and only if b is nilpotent with cyclic defect groups.

Affiliated with

Also associated with

No associations

Rating

On the Cartan matrix of Mackey algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Cartan matrix of Mackey algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Cartan matrix of Mackey algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-234089