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A splitting algebra of
In this subsection we assume that
is a field of characteristic
. Let
where
. It is a splitting algebra of
, as the following lemma tells.
Lemma 5
The algebra
acts on
. In other words, there exists a representation
of
on
.
where elements
of
are defined (using notation in Lemma
1
) as follows.
The representation
may be extended to the following isomorphism.
Put
. Then it is easy to show that elements
satisfy the relation of generators of the algebra
as in Lemma
1
.
ARRAY(0x8ececbc)
2003/3/3