Degree four cohomological invariants for certain central simple algebras

JOURNAL OF ALGEBRA

卷:527

Article

Sivatski, A. S.¹ 

[1] Univ Fed Rio Grande do Norte, Dept Matemat, Natal, RN, Brazil

关键词: Brauer group;    Biquaternion;    Cup-product;    Cyclic elements;    Divided power operation;   

DOI  :  10.1016/j.jalgebra.2019.01.037

来源: Elsevier

【 摘 要 】

Let F be a field, char F not equal 2. In the first section of the paper we prove that if A = (a,b) + (c, d) is a biquaternion algebra divisible by 2 in the Brauer group Br(F), and <<-1, - 1 >>(F) = 0, then the symbol (a, b, c, d) is an element of H-4 (F, Z/2Z) is an invariant, i.e. it does not depend on the decomposition of A into a sum of two quaternions. In the second section we construct an invariant p in H-4(F, Z/2Z) for elements C+alpha is an element of Br-4(F), where C is cyclic of degree at most 4, and alpha is an element of Br-2(F). In the case root-1 is an element of F* we extend the invariant p to elements D + alpha is an element of Br-4(F), where ind D <= 4 and alpha is an element of Br- 2(F). (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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