Enumerating algebras over a finite field

Document Type: Research Paper

Author

Oxford University Mathematical Institute

Abstract

‎We obtain the PORC formulae for the number of non-associative algebras‎ ‎of dimension 2‎, ‎3 and 4 over the finite field GF$(q)$‎. ‎We also give some‎ ‎asymptotic bounds for the number of algebras of dimension $n$ over GF$(q)$‎.

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