|
Let C be a Clifford algebra of a quadratic space V and suppose
that e1, e2, ..., en is a basis for V. Let C_ + be the
subspace of linear combinations of products of an even number of basis
elements and let C_ - be the subspace of linear combinations of
products of an odd number of basis elements. Then C_ + is a subalgebra
and C is the direct sum of C_ + and C_ -. The main involution
of C is the automorphism J such that J(u) = u if u∈C_ + and
J(u) = - u if u∈C_ -.
The main involution of the Clifford algebra C.
The mapping C to C which reverses the multiplication is
an antiautomorphism whose square is the identity; it is called the
main antiautomorphism of C.
The main antiautomorphism of C. The first time this function
is invoked it sets the attribute antiAutMat of C to the
matrix defining this map.
[Next][Prev] [Right] [Left] [Up] [Index] [Root]
|