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Isomorphism problems in algebra
Intervenant(s) : Nitin SAXENA (Department of Computer Science and Engineering, IIT Kanpur, India)Finite dimensional commutative algebras are rich structures. It is a natural question to study the computational complexity of testing their isomorphism. In this talk we will relate this to the corresponding question of other mathematical objects, namely, quadratic forms, cubic forms and graphs.
While the theory of quadratic forms is quite well developed (in the last century), the case of cubic forms is far more involved. We show that cubic forms equivalence is as hard as F-algebra isomorphism, which is as hard as graph isomorphism. Also, the 'hardness' of these questions seem to depend on the underlying field F. We will see that for the complex and the finite field F, the problems seem 'easier' than that over the field of rationals.
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