Abstract
Let p be a prime and K a p-adic field (a, finite extension of the field of p-adic numbers Q(p)). We employ the main results in [12] and the arithmetic of elliptic curves over K to reduce the problem of classifying 3-dimensional non-associative division algebras (up to isotopy) over K to the classification of ternary cubic forms over K (up to equivalence) With 110 non-trivial zeros over K. We give an explicit solution to the latter problem, which we then relate to the reduction type of the jacobian of H.
This result completes the classification of 3-dimensional non-associative division algebras over number fields done in [12]. These algebras are, use:fill for the construction of space-time codes, which are used to make communications over multiple-transmit; antenna systems more reliable.