334 



Rl 



a-^^: I ) (compli- 

 =1 «-yH- ) cated) 

 <^-<i''t (15) 



(t - f- z:z n - (\ 



cycl. 1,2,3,4. 



= r2 = k^ = +l 



^: - 



""'^= + cated) 



h!2 = +l 



«-y 



it- ff: identity 



(t- f. identity 



= ! cycl. 1,2, 3,4 



(compli- 



«- y =ii — (3 (16) 



The {Jiialilies a - (i are complicated ones in this case, i. e. dnalising 

 leads say for n - ^i from e, to e'/, from e', to - e,, from — e; to — e';. 

 and from — eV again to e, . This complicated duality always exists 

 for 11 even ^), as long as one of the units is not privileged. If one 

 of the units is privileged, or, to put it otherwise, if we dei-ive the 

 system belonging to the group, leaving invariant the quadratic form 



- a/ + a/ + . . . f a,._i« 



we find, when classifying up to the orthogonal groups inclusive, 

 the system : 



The complicated duality exists also in Grassmann's Ausdehnungslehre for 

 n even. 



