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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On crossed products of Hopf algebras
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by Maria E. Lorenz and Martin Lorenz PDF
Proc. Amer. Math. Soc. 123 (1995), 33-38 Request permission

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
  • Eiichi Abe, Hopf algebras, Cambridge Tracts in Mathematics, vol. 74, Cambridge University Press, Cambridge-New York, 1980. Translated from the Japanese by Hisae Kinoshita and Hiroko Tanaka. MR 594432
  • Susan Montgomery, Hopf algebras and their actions on rings, CBMS Regional Conference Series in Mathematics, vol. 82, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1993. MR 1243637, DOI 10.1090/cbms/082
  • Joseph J. Rotman, An introduction to homological algebra, Pure and Applied Mathematics, vol. 85, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. MR 538169
  • Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • 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