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Proceedings of the American Mathematical Society

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

 
 

 

On crossed products of Hopf algebras


Authors: Maria E. Lorenz and Martin Lorenz
Journal: Proc. Amer. Math. Soc. 123 (1995), 33-38
MSC: Primary 16E10; Secondary 16S40, 16W30
DOI: https://doi.org/10.1090/S0002-9939-1995-1227522-6
MathSciNet review: 1227522
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Abstract: Let $ B = A{\char93 _\sigma }H$ denote a crossed product of the associative algebra A with the Hopf algebra H. We investigate the weak dimension and the global dimension of B and show that $ {\text{wdim}}\;B \leq {\text{wdim}}\;H + {\text{wdim}}\;A$ and $ {\text{l.gldim}} \; B \leq {\text{r.gldim}} \; H + {\text{l.gldim}} \; A$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1227522-6
Keywords: Hopf algebra, crossed product, global dimension, weak dimension, projective dimension, flat dimension, von Neumann regular ring, semisimple ring
Article copyright: © Copyright 1995 American Mathematical Society

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