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Tensor products of positive definite quadratic forms, VII
Published online by Cambridge University Press: 22 January 2016
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In this paper we generalize results of the third paper of this series. As a corollary we can show the following: Let Li (1 ≤ i ≤ n) be a positive definite quadratic form which is equivalent to one of Cartan matrices of Lie algebras of type An (n ≥ 2), Dn (n ≥ 4), E6, E7, E8 and assume that is positive definite quadratic forms and satisfies that rk Mt ≥ 2 and implies rk K or rk L = 1. Then we have n = m and Lt is equivalent to a constant multiple of Ms(i) for some permutation s. Therefore we get the uniqueness of decompositions with respect to tensor products in this case.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1984
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