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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Crossed simplicial groups and their associated homology
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by Zbigniew Fiedorowicz and Jean-Louis Loday PDF
Trans. Amer. Math. Soc. 326 (1991), 57-87 Request permission


We introduce a notion of crossed simplicial group, which generalizes Connes’ notion of the cyclic category. We show that this concept has several equivalent descriptions and give a complete classification of these structures. We also show how many of Connes’ results can be generalized and simplified in this framework.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 326 (1991), 57-87
  • MSC: Primary 18F25; Secondary 18D05, 19D55, 20F36, 55U10
  • DOI:
  • MathSciNet review: 998125