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Proceedings of the American Mathematical Society

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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
MathSciNet review: 1227522
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Abstract: Let $B = A{\# _\sigma }H$ 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 ${\text {l.gldim}} \; B \leq {\text {r.gldim}} \; H + {\text {l.gldim}} \; A$.

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

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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