Then acts by left multiplication on the product of coset spaces.
2.
The free group acts by left multiplication on the semi-infinite words.
3.
Any acting on itself by left multiplication.
4.
The left multiplication by quaternions is linear.
5.
In the case when the endomorphism ring, where each endomorphism arises as left multiplication by a fixed ring element.
6.
An equivalent definition of a principal-bundle is as a-bundle with fiber where the structure group acts on the fiber by left multiplication.
7.
The group G acts on itself by left multiplication : the action of each k \ in G takes each g \ in G to kg.
8.
There is an obvious one-dimensional quaternionic vector space, namely the space "'H "'of quaternions themselves under left multiplication.
9.
Indeed, it represents the left multiplication action of the versor on quaternions that preserves the plane ? and the corresponding great circle of 3-vectors.
10.
A further complication with quaternion representations of fermions is that there are two types of multiplication : left multiplication and right multiplication which must be taken into account.
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