The number of nonisomorphic non-associative algebras over a
finite field
In this paper, we derive explicit formulas for the number of
nonisomorphic two-dimensional nonassociative algebras, possibly without
a unit, over a finite field. The proof combines the first author's
general classification theory of two-dimensional nonassociative algebras
over arbitrary base fields with elementary counting arguments addressed
to the problem of determining the number of orbits of a finite set acted
upon by the group of integers mod 2.
The number of two-dimensional "division" algebras over a finite field
will also be determined.
(This paper has appeared in Result. Math. 45 (2004), 137-152)
Holger P. Petersson < holger.petersson@fernuni-hagen.de >
Matthias Scherer < math.scherer@bluemail.ch >