Classification of commutative algebras and tube realizations of hyperquadrics
Abstract
In this paper we classify up to affine equivalence all local tube realizations of real hyperquadrics in Cn. We show that this problem can be reduced to the classification, up to isomorphism, of commutative nilpotent real and complex algebras. We also develop some structure theory for commutative nilpotent algebras over arbitrary fields of characteristic zero.
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