2 edition of **Monoidal functors, species, and Hopf algebras** found in the catalog.

Monoidal functors, species, and Hopf algebras

Marcelo Aguiar

- 33 Want to read
- 5 Currently reading

Published
**2010**
by American Mathematical Society in Providence, R.I
.

Written in English

**Edition Notes**

Includes bibliographical references and index.

Statement | Marcelo Aguiar, Swapneel Mahajan |

Series | CRM monograph series / Centre de recherches mathématiques, Montréal -- v. 29 |

Contributions | Mahajan, Swapneel Arvind, 1974- |

Classifications | |
---|---|

LC Classifications | QA613.8 .A385 2010 |

The Physical Object | |

Pagination | p. cm. |

ID Numbers | |

Open Library | OL24438301M |

ISBN 10 | 9780821847763 |

LC Control Number | 2010025240 |

OCLC/WorldCa | 645708042 |

This work very nicely complements the other texts on Hopf algebras and is a welcome addition to the literature.” ―Jan E. Grabowski, Mathematical Reviews, July, "In this book, Underwood chooses to introduce Hopf algebras in a manner most natural to a reader whose knowledge of algebra does not extend much beyond a first year graduate Cited by: AFAIU, the Hopf algebra way to compute a Feynman diagram consists of cutting it into two in all possible ways, and then reducing the calculation to the two subdiagrams, which are simpler. The Hopf algebra structure is a way to understand and equivalently reformulat the structure of the counterterm in the BPHZ regularization g: species.

An introduction to Category Theory. The book is aimed primarily at the beginning graduate gives the de nition of this notion, goes through the various associated gadgetry such as functors, natural transformations, limits and colimits, and then explains adjunctions. monoidal categories, Monoidal functors, equivalence of monoidal. In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism satisfying a certain property. The representation theory of a Hopf algebra is particularly nice, since the.

hopf algebras and combinatorics san francisco state university. universidad de los andes federico ardila m. The topic. We will study Hopf algebras, with an emphasis on their connections with combinatorics. Hopf algebras are spaces with a notion of multiplication and comultiplication, which satisfy certain compatibility relations. Hopf Algebras and Tensor Categories: International Conference July , , University of Almeria, Almeria, Spain American Mathematical Society NicolÃ¡s Andruskiewitsch, Juan Cuadra, Blas Torrecillas, Juan Cuadra, Blas Torrecillas, Nicolas Andruskiewitsch.

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Buy Monoidal Functors, Species and Hopf Algebras (Crm Monograph Series) on FREE SHIPPING on qualified orders Monoidal Functors, Species and Hopf Algebras (Crm Monograph Series): Marcelo Aguiar, Swapneel Mahajan: : BooksCited by: These functors are bilax monoidal and thus translate Hopf monoids in species to graded Hopf algebras.

This functorial construction of Hopf algebras encompasses both quantum groups and the Hopf algebras of recent prominence in the combinatorics literature. Monoidal Functors, Species and Hopf Algebras Marcelo Aguiar Swapneel Mahajan Department of Mathematics Texas A&M University College Station, TX USA E-mail address: [email protected] Hopf lax monoidal functors 88 An alternative description of bilax monoidal functors 97 Adjunctions of monoidal functors These functors are bilax monoidal and thus translate Hopf monoids in species to graded Hopf algebras.

This functorial construction of Hopf algebras encompasses both quantum groups and the Hopf algebras of recent prominence in the combinatorics literature. The monograph opens a vast new area of research. BibTeX @MISC{Aguiar_society, author = {M. Aguiar and S. Mahajan and Coxeter Groups and Kenneth Brown and Stephen Chase and Andre Joyal and Crm Monograph Series and C.

Balteanu and Z. Fiedorowicz and R. Vogt and Iterated Monoidal Cate}, title = {Society, [4], Monoidal functors, species and Hopf algebras. With forewords by}, year = {}}.

BibTeX @MISC{Aguiar_monoidalfunctors, author = {Marcelo Aguiar and Swapneel Mahajan}, title = {Monoidal functors, species and Hopf algebras}, year = {}}. This entry is about the book. Marcelo Aguiar, Swapneel Mahajan, Monoidal Species, Species and Hopf Algebras, finished Maypages.

on monoidal functors, combinatorial species and Hopf algebras. related entries. Hopf monoid; partition; shuffle. They have been extensively studied in Aguiar{Mahajan’s page book \Monoidal Functors, Species and Hopf Algebras," which is rmly categorical and highly abstract.

Ardila{Aguiar seem to go out of their way to avoid categorical language, and I’ll now largely follow their Size: KB. hopf algebras san francisco state university universidad de los andes federico ardila hopf cafe.

homework. lectures. people. projects. syllabus. texts. The following is a list of books and other resources that you might find helpful. Monoidal categories in, and linking, geometry and algebra a few now coming from our book [78] for which he was the Technical Editor.

Along with the standard references [58] and [12], our book provides a good supplement to 2 Monoidal categories, Hall algebras and representation theory For the "state-of-the-art" on combinatorial Hopf algebras, I would look at: Marcelo Aguiar's web site.

and in particular the page book which he and Swapneel Mahajan have written entitled "Monoidal functors, species and Hopf algebras". I don't actually work on these myself though, so perhaps others will have further more precise suggestions.

The book is of interest to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads. Keywords monoidal categories Hopf algebras Hopf monads 3-manifold invariants topological quantum field theory state sums. In the literature often the term “monoidal functor” refers by default to what in def.

is called a strong monoidal functor. With that convention then what def. calls a lax monoidal functor is called a weak monoidal functor. Remark. Lax monoidal functors are the lax morphisms for an appropriate Monoidal functors, species and Hopf algebras.

Hopf group algebras in [Turaev ,Zunino ,Caenepeel-De Lombaerde ]), Hopf categories in [Batista-Caenepeel-Vercruysse ] and Hopf polyads in [Brugui eres ] can be seen as Hopf monads in suitable monoidal bicategories. You could also look at Propositionand the commutative diagram on page 15 of Aguiar and Mahajan's book "Monoidal Functors, Species, and Hopf Algebras".

Marcelo Aguiar and Swapneel Mahajan, Monoidal functors, species and Hopf algebras, CRM Monograph Series, vol. 29, American Mathematical Society, Providence, RI, With forewords by Kenneth Brown and Stephen Chase and André Joyal. MR (g)Cited by: 9.

This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current 1 introduces monoidal categories and several of their classes, including rigid, pivotal.

On the duality of generalized Lie and Hopf algebras. an adjoint pair of braided monoidal functors can be lifted to an adjoint pair between categories of Hopf algebras. This leads us to an Missing: species.

Strong forms of linearization for Hopf monoids in species. Book. Mar ; Marcelo Aguiar Monoidal Functors, Species and Hopf Algebras, Volume 29 of CRM Mono-graph Series. American. Monoidal functors. MacLane's strictness theorem: 3: MacLane coherence theorem.

Rigid monoidal categories. Invertible objects. Tensor and multitensor categories: 4: Tensor product and tensor functors. Unit object.

Grothendieck rings. Groupoids. Finite abelian categories. Fiber functors. Coalgebras: 5: Bialgebras and Hopf algebras: 6: Quantum. For a pair of liftable, Lie-liftable functors (L, R) between symmetric monoidal categories C and D, we then obtain a diagram of (all covariant) adjoint functors For any Lie algebra K in D, there is a natural isomorphism of Hopf algebras in C L ¯ ̲ U K ≅ U L ˜ K and for any Hopf algebra H in C, then there is a natural isomorphism of Lie Cited by: 2.The category of strict polynomial functors inherits an internal tensor product from the category of divided powers.

To investigate this monoidal structure, we consider the category of representations of the symmetric group S d which admits a tensor product coming from its Hopf algebra structure.

It is classical that there exists a functor F from the category of strict polynomial functors to Cited by: 4.Hopf algebras are constructed from aﬃne group schemes), Lie theory (the universal enveloping algebra of a Lie algebra is a Hopf algebra), Galois theory and separable ﬁeld extensions (in relation with so-called Hopf-Galois theory), graded ring theory (one constructs a Hopf algebra from a graded ring and there is a strong relation.