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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1978-0491794-6
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

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


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0491794-6
Keywords: Hopf algebras
Article copyright: © Copyright 1978 American Mathematical Society