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Basic Algebra:
The
word sedenion is derived from sexdecim, meaning sixteen.
A sedenion is a hypercomplex number constituted from 16 basal elements.
A set of sedenions form an algebra, S.
If S, T, V represent three sedenions the algebra is
-
Non commutative : ST is not necessarily equal
to TS
-
Non associative : S(TV) is
not necessarily equal to (ST)V
-
Non alternative : S(ST)
is not necessarily equal to S2T
-
Power associative : Sn
Sm = Sn+m
Furthermore it is
-
Not a composition algebra : n(ST) is not necessarily
equal to n(S) n(T) , where the norm of S is defined as
n(S) = S S* = S*S ,
S* is a conjugate of S
-
Not a division algebra : i.e. there are
zero divisors ;
There are sedenions S and
T , neither of them zero, but ST = 0 = TS.
Our
Publication
Sedenion: Algebra and analysis
by K.Imaeda & Mari Imaeda
Abstract
A 16-dimensional Cayley-Dickson
algebra is presented. Its unique algebraic properties, its zero divisors,
and the solutions to a general linear equation are found. A theory
of function is developed in terms of the regularity (monogenicity) conditions
and some such functions are constructed.
4/1999 : Accepted for publication in Applied
Mathematics and Computation.
Publication date : 10/2000, Vol. 115/2-3,
pp77-88 |
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Octonions
&
Sedenions