@article{1463275,
      author = {Kashaev, Rinat,},
      url = {http://library.usi.edu/record/1463275},
      title = {A course on Hopf algebras /},
      abstract = {This textbook provides a concise, visual introduction to  Hopf algebras and their application to knot theory, most  notably the construction of solutions of the Yang-Baxter  equations. Starting with a reformulation of the definition  of a group in terms of structural maps as motivation for  the definition of a Hopf algebra, the book introduces the  related algebraic notions: algebras, coalgebras,  bialgebras, convolution algebras, modules, comodules. Next,  Drinfel'd's quantum double construction is achieved through  the important notion of the restricted (or finite) dual of  a Hopf algebra, which allows one to work purely  algebraically, without completions. As a result, in  applications to knot theory, to any Hopf algebra with  invertible antipode one can associate a universal invariant  of long knots. These constructions are elucidated in  detailed analyses of a few examples of Hopf algebras. The  presentation of the material is mostly based on multilinear  algebra, with all definitions carefully formulated and  proofs self-contained. The general theory is illustrated  with concrete examples, and many technicalities are handled  with the help of visual aids, namely string diagrams. As a  result, most of this text is accessible with minimal  prerequisites and can serve as the basis of introductory  courses to beginning graduate students.},
      doi = {https://doi.org/10.1007/978-3-031-26306-4},
      recid = {1463275},
      pages = {1 online resource (xv, 165 pages).},
}