An identity on algebras over a Hopf algebra
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- by Stavros Papastavridis PDF
- Proc. Amer. Math. Soc. 70 (1978), 87-88 Request permission
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 \[ ax \cdot y = \Sigma {( - 1)^{\deg x \cdot \deg a''}}a’(x \cdot \chi (a'')y).\]References
- S. Papastavridis, A formula for the obstruction to transversality, Topology 11 (1972), 415–416. MR 312497, DOI 10.1016/0040-9383(72)90036-5 —, The Arf invariant of manifolds with few non-zero Stiefel-Whitney classes, Ph. D. Thesis, Princeton Univ., Princeton, N. J., 1974.
- N. E. Steenrod, The cohomology algebra of a space, Enseign. Math. (2) 7 (1961), 153–178 (1962). MR 160208
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 70 (1978), 87-88
- MSC: Primary 16A24; Secondary 57F05
- DOI: https://doi.org/10.1090/S0002-9939-1978-0491794-6
- MathSciNet review: 0491794