Abstract:
Let G be a finite group acting by automorphism on
a lattice
A , and hence on the group algebra S=k[A]
. The algebra of
G-invariants in S is called an algebra of
multiplicative
invariants.
We present an explicit version of a result of Farkas stating that
multiplicative invariants of finite reflection groups are
semigroup algebras.
In the longer (unpublished) version below, we also show that
multiplicative invariants arising from fixed point free actions
are never semigroup algebras. In particular, this holds whenever
G has odd prime order.
Electronic Preprint:
postscript file
short
version (117KB) and
long
version (189KB)
dvi file
short
version (47KB) and
long
version (68KB)
pdf file
short version (118KB) and
long version (246KB).
GAP code for Example 2.7.2:
This example (and others) can be done
by reading
this file
into GAP. Save the file as weights, for example,
start GAP from the
directory where you saved the file, and type
Read("weights");
at the GAP command line. The file weights in turn reads in
a file
To see the complete GAP session,
click here.
Example 3.6.1 (done by hand in the paper) can also be handled in this way,
by changing the first line in weights to
i:=2;