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Proceedings of the American Mathematical Society

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An identity on algebras over a Hopf algebra

Author: Stavros Papastavridis
Journal: Proc. Amer. Math. Soc. 70 (1978), 87-88
MSC: Primary 16A24; Secondary 57F05
MathSciNet review: 0491794
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Abstract: Let A be a connected Hopf algebra which has an associative comultiplication $ \psi :A \to A \otimes A$. Let $ \chi :A \to A$ be the canonical conjugation on A. Let M be a graded algebra over the Hopf algebra A. If $ x,y \in M,\psi (a) = \Sigma a' \otimes a''$, then we have the identity

$\displaystyle ax \cdot y = \Sigma {( - 1)^{\deg x \cdot \deg a''}}a'(x \cdot \chi (a'')y).$

References [Enhancements On Off] (What's this?)

  • [1] S. Papastavridis, A formula for the obstruction to transversality, Topology 11 (1972), 415-416. MR 0312497 (47:1054)
  • [2] -, The Arf invariant of manifolds with few non-zero Stiefel-Whitney classes, Ph. D. Thesis, Princeton Univ., Princeton, N. J., 1974.
  • [3] N. Steenrod, The cohomology algebra of a space, Enseignement Math. 7 (1961), 153-177. MR 0160208 (28:3422)

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Keywords: Hopf algebras
Article copyright: © Copyright 1978 American Mathematical Society

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