Event № 357
If one seeks an associative algebra which corresponds canonically to a Euclidean space E (or to any vector space with a quadratic form Q) - canonically means that we refrain from "choosing", say a basis/coordinate system - an option is the Clifford algebra of the space, defined as the associative algebra generated by E, with the relations that the square in the algebra of each vector v in E equals Q(v)1. This algebra contains a plethora of interesting members and structures. Focusing mainly on the Euclidean 4-space, we shall describe its basics and try to stroll in its garden and pick some flowers. In particular, we shall encounter objects mentioned in Maria Elena Luna-Elizarraras' lecture: the 2-dim extension of the reals by a k satisfying k2=1, and bi-quaternions.