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Published in:
2006 | OriginalPaper | Chapter
Equivalence of -Algebras and Cubic Forms
Authors : Manindra Agrawal, Nitin Saxena
Published in: STACS 2006
Publisher: Springer Berlin Heidelberg
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We study the isomorphism problem of two “natural” algebraic structures –
$\mathbb{F}$
-algebras and cubic forms. We prove that the
$\mathbb{F}$
-algebra isomorphism problem reduces in polynomial time to the cubic forms equivalence problem. This answers a question asked in [AS05]. For finite fields of the form
$3 \Lambda(\#\mathbb{F} - 1)$
, this result implies that the two problems are infact equivalent. This result also has the following interesting consequence:
Graph Isomorphism
${\leq}^P_m$
$\mathbb{F}$
-algebra Isomorphism
${\leq}^P_m$
Cubic Form Equivalence.