Bimodule structure of central simple algebras

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• 作者：Eliyahu Matzri^a ; ^{elimatzri@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Louis H. Rowen^a ; ^{rowen@math.biu.ac.il" class="auth_mail" title="E-mail the corresponding author} ; David Saltman^b ; ^{saltman@idaccr.org" class="auth_mail" title="E-mail the corresponding author} ; Uzi Vishne^a ; ^{vishne@math.biu.ac.il" class="auth_mail" title="E-mail the corresponding author}
• 关键词：16K20
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：471
• 期：Complete
• 页码：454-479
• 全文大小：493 K

文摘

For a maximal separable subfield K of a central simple algebra A, we provide a semiring isomorphism between K–K-sub-bimodules of A and H–H  -sub-bisets of G=Gal(L/F)$G=\mathrm{Gal}(L/F)$, where F=Cent(A)$F=\mathrm{Cent}(A)$, L   is the Galois closure of 8e1e8" title="Click to view the MathML source">K/F$K/F$, and H=Gal(L/K)$H=\mathrm{Gal}(L/K)$. This leads to a combinatorial interpretation of the growth of 58469922bd22ae11230" title="Click to view the MathML source">dim_K⁡((KaK)ⁱ)${\dim }_K({(KaK)}^i)$, for fixed 8e1526634a648c51c0c04" title="Click to view the MathML source">a∈A$a\in A$, especially in terms of Kummer subspaces.