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作者 Bohm, Gabriella, author
書名 Hopf algebras and their generalizations from a category theoretical point of view / Gabriella Bohm
出版項 Cham, Switzerland : Springer, [2018]
2018
國際標準書號 9783319981369
3319981366
國際標準號碼 10.1007/978-3-319-98137-6
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA613.8 B64 2018    在架上    30340200560278
說明 xi, 163 pages : illustrations ; 24 cm
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
Hungarians lcdgt
Women lcdgt
系列 Lecture notes in mathematics, 0075-8434 ; 2226
Lecture notes in mathematics (Springer-Verlag) ; 2226. 0075-8434
附註 Includes bibliographical references (pages 155-159) and index
Lifting to Eilenberg-Moore categories -- (Hopf) bimonads -- (Hopf) bialgebras -- (Hopf) bialgebroids -- Weak (Hopf) bialgebras -- (Hopf) bimonoids in duoidal categories -- Solutions to the exercises
"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, semi-Hopf group algebras, small categories, and categories enriched in coalgebras. Graduate students and researchers in algebra and category theory will find this book particularly useful. Including a wide range of illustrative examples, numerous exercises, and completely worked solutions, it is suitable for self-study"--Page 4 of cover
主題 Hopf algebras
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