Here is the problem:
Let
be a field and
a quadratic space with an anisotropic form
not representing
. Show that if
and
are not both zero, then
is an invertible element in the Clifford algebra
.
I'm not really sure how to start this problem. I don't fully understand Clifford algebras, so I don't even really know what invertible elements even look like. I understand the definition -
, where I is the ideal generated by
- but I don't understand the resulting algebra (except when
is a binary or nonzero unary form).
Any help is appreciated.