A duality theorem in Hopf algebras and its application to Morava \(K\)-theory of \(B\mathbb{Z}/p^r\)
type: Item
instance of: scholarly article
title: A duality theorem in Hopf algebras and its application to Morava \(K\)-theory of \(B\mathbb{Z}/p^r\)
zbMATH Open document ID: 0906.55002
author: Kakhaber Kordzaya
author: Goro Nishida
published in: Journal of Mathematics of Kyoto University
publication date: 1999-02-11T00:00:00Z
review text: Let \(A\) be a bicommutative Hopf algebra over a ring \(R\), \(S\) a commutative \(R\) algebra, \(A^*= \Hom_{R\text{-module}} (A,R)=\) the dual of \(A\), and \(G(A)(S)= \Hom_{R\text{-algebra}} (A,S)\). The authors show that for certain \(R\), \(S\) there is an isomorphism \(G(A)(S)\equiv G(A^*)(S)\). This is applied to the particular case of the Hopf algebra \(A=\overline{K(n)}^0_{O_L} (B\mathbb{Z}/p^r)\) where \(O_L\) is the ring of integers in a finite extension of the \(p\)-adic numbers and \(\overline{K(n)}^*_{O_L}(\;)=\overline{K(n)}^*(\;)\otimes O_L\) denotes p-adic Morava K-theory of period 2 with \(O_L\) coefficients. Using this it is shown that the group of homotopy classes of ring spectra maps \((B\mathbb{Z}/p^r)_+ \rightarrow \overline{K(n)}_{O_L} \) is isomorphic to \((\mathbb{Z}/p^r)^n\).
reviewed by: Keith Johnson
Mathematics Subject Classification ID: 55N20
Mathematics Subject Classification ID: 57T05
Mathematics Subject Classification ID: 55N15
zbMATH DE Number: 1062464
zbMATH Keywords: Hopf algebra
zbMATH Keywords: Morava \(K\)-theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518450
OpenAlex ID: W1608058001
DOI: 10.1215/KJM/1250518450
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description: scientific article; zbMATH DE number 1062464