书目名称 | Hopf Algebras and Their Generalizations from a Category Theoretical Point of View | 编辑 | Gabriella Böhm | 视频video | | 概述 | First book to provide a unified category theoretical description of apparently different generalizations of Hopf algebras (including Hopf algebroids, weak Hopf algebras, and Hopf bimonoids in duoidal | 丛书名称 | Lecture Notes in Mathematics | 图书封面 |  | 描述 | .These lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending the range of applications..Since Sweedler‘s work in the 1960s, Hopf algebras have earned a noble place in the garden of mathematical structures. Their use is well accepted in fundamental areas such as algebraic geometry, representation theory, algebraic topology, and combinatorics. Now, similar to having moved from groups to groupoids, it is becoming clear that generalizations of Hopf algebras must also be considered. This book offers a unified description of Hopf algebras and their generalizations from a category theoretical point of view. The author applies the theory of liftings to Eilenberg–Moore categories to translate the axioms of each considered variant of a bialgebra (or Hopf algebra) to a bimonad (or Hopf monad) structure on a suitable functor. Covered structures include bialgebroids over arbitrary algebras, in particular weak bialgebras, and bimonoids in duoidal categories, such as bialgebras over commutative rings, se | 出版日期 | Book 2018 | 关键词 | MSC (2010): 16T10, 16T05, 18C15, 18D10, 18D15; bialgebra; Hopf algebra; bialgebroid; Hopf algebroid; weak | 版次 | 1 | doi | https://doi.org/10.1007/978-3-319-98137-6 | isbn_softcover | 978-3-319-98136-9 | isbn_ebook | 978-3-319-98137-6Series ISSN 0075-8434 Series E-ISSN 1617-9692 | issn_series | 0075-8434 | copyright | Springer Nature Switzerland AG 2018 |
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