Clifford division algebras and anisotropic quadratic forms: two counterexamples
1986 ◽
Vol 28
(2)
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pp. 227-228
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Keyword(s):
In a recent paper [3], D. W. Lewis proposed the following conjecture. (The notation is the same as that in [2] and [3].)Conjecture. Let F be a field of characteristic not 2 and let a1, b1…, an, bn ∈ Fx. The tensor product of quaternion algebrasis a division algebra if and only if the quadratic form over Fis anisotropic.This equivalence indeed holds for n = 1 as is well known [2, Theorem 2.7], and Albert [1] (see also [4, §15.7]) has shown that it also holds for n = 2. The aim of this note is to provide counterexamples to both of the implications for n ≥ 3.
2014 ◽
Vol 150
(12)
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pp. 2073-2094
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1981 ◽
Vol 89
(2)
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pp. 225-235
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1981 ◽
Vol 31
(2)
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pp. 175-188
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1953 ◽
Vol 10
(1)
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pp. 13-15
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1963 ◽
Vol 15
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pp. 412-421
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2020 ◽
Vol 102
(3)
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pp. 374-386
Keyword(s):