CONTENTS

**Division Algebras,
Lie Algebras, Lie Groups and Spinors**

### 14. Complexified Octonions: a Totally Cool Mathematical Result

Let me stress that
this is a purely mathematical result. With respect to the Lie group

SU(3) generated from the Lie algebra above, **W** transforms as the direct
sum of an

SU(3) singlet, triplet, antisinglet, and antitriplet. The corresponding SU(3)
charges

AND U(1) charges are exactly those we encounter in the standard model of quarks

and leptons. The standard model also has an SU(2) internal symmetry. That and

much more are covered in the pdf (see bottom of Contents), and especially in
the
book.

Personally I find this mathematical result and physical correspondence totally
cool.

Cheers.

CONTENTS