Seminar series
Date
Fri, 18 Oct 2013
Time
14:00 -
15:00
Location
L3
Speaker
Radha Kessar
Organisation
City University London
We investigate symmetric quotient algebras of symmetric algebras,
with an emphasis on finite group algebras over a complete discrete
valuation ring R with residue field of positive characteristic p. Using elementary methods, we show that if an
ordinary irreducible character of a finite group gives
rise to a symmetric quotient over R which is not a matrix algebra,
then the decomposition numbers of the row labelled by the character are
all divisible by p. In a different direction, we show that if is P is a finite
p-group with a cyclic normal subgroup of index p, then every ordinary irreducible character of P gives rise to a
symmetric quotient of RP. This is joint work with Shigeo Koshitani and Markus Linckelmann.