商环谱上的Clifford代数
Clifford algebras from quotient ring spectra
摘要：
给出了偶E-无限环谱的正则商环谱的同调代数和上同调代数的自然刻画。我们证明了该同调是一个Clifford代数，它关于一个自然地与商环谱F相关联的双线性型。为了确定上同调代数，我们首先确定F的导子，然后证明上同调代数在导子模上同构于外代数。我们将详细讨论摩拉瓦K理论的例子。
英文摘要：
We give natural descriptions of the homology and cohomology algebras of regular quotient ring spectra of even E-infinity ring spectra. We show that the homology is a Clifford algebra with respect to a certain bilinear form naturally associated to the quotient ring spectrum F. To identify the cohomology algebra, we first determine the derivations of F and then prove that the cohomology is isomorphic to the exterior algebra on the module of derivations. We treat the example of the Morava K-theories in detail.
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