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The Brauer-Long group of a Hopf algebra over a commutative ring is discussed in Part III. This provides a link between the first two parts of the volume and is the first time this topic has been discussed in a : Springer Netherlands. Buy Brauer Groups, Hopf Algebras and Galois Theory (K-Monographs in Mathematics) (Volume 4) on FREE SHIPPING on qualified orders Brauer Groups, Hopf Algebras and Galois Theory (K-Monographs in Mathematics) (Volume 4): Stefaan Caenepeel: : BooksCited by: Book reviews.
BRAUER GROUPS, HOPF ALGEBRAS AND GALOIS THEORY (K‐Monographs in Mathematics 4) Victor Snaith. University of Southampton. Search for more papers by this author. Victor Snaith. University of Southampton. Search for more papers by this author. First published: 23 December Cited by: 6. Cohomological interpretation of the Brauer group -- II.
Hopf algebras and Galois theory. Hopf algebras. Galois objects. Cohomology over Hopf algebras. The group of Galois (co)objects. Some examples -- III.
The Brauer-Long group of a commutative ring. H-Azumaya algebras. The Brauer-Long group of a commutative ring. THE BRAUER GROUP OF A HOPF ALGEBRA i. ´(ab) = P a(0)b(0) ›a(1)b(1), ii. ´(1) = 1 ›1.
An H-dimodule algebra A is an H-dimodule and a k-algebra which is both an H-module algebra and an H-comodule e that H is both com- mutative and cocommutative.
Let A and B be two H-dimodule smash product A#B is deﬁned as follows: A#B = A › B as a k-module andCited Brauer Groups 5. Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra.
The development of the theory is carried out in such a way that the connection to the theory of the Brauer group in Part I Author: Stefaan Caenepeel. Hopf Algebra Direct Brauer Groups Galois Extension Module Algebra Smash Product These keywords were added by machine and not by the authors.
This process is experimental and the keywords may be updated as the learning algorithm by: Abstract. We show that the Brauer group BM (k, Hν, Rs,β) of the quasitriangular Hopf algebra (Hν, Rs,β) is a direct product of the additive group of the field k and the classical Brauer group associated to the bicharacter θs on defined by θs (x, y)= ωsxy, with ω a 2 ν th root of by: Galois theories, Hopf algebras, and semiabelian categories.
Here is a very brief indication of the origins of those connections. Hopf algebras arrived to the Galois theory of rings as early as the s — independently of, but in fact similarly to, the way in which algebraic group schemes were introduced to the theory of etaleFile Size: 2MB.
An algebra is a vector space V over a eld k together with a k- bilinear product of vectors under which V is a ring. A certain class of algebras, called Brauer algebras - algebras which split over a nite Galois extension - appear in many sub elds of abstract algebra, including K-theory and class eld Size: KB.
That ring need not be a eld of characteristic zero. Here are some examples. In number theory, groups arise as Galois groups of eld extensions, giving rise not only to representations over the ground eld, but also to integral representations over rings of integers (in case the elds are number elds).File Size: 1MB.
Brauer group. In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras.
It was defined by the algebraist Richard Brauer. Let (H,R) be a finite dimensional quasitriangular Hopf algebra over a field k, and MH the representation category of H.
In this paper, we study the br. Brauer groups, Hopf algebras Program Book of abstracts. Brauer groups, Hopf algebras and monoidal categories - Stef Fest 3 Dear Participant, We welcome you at the University of Turin to participate at the conference \Brauer groups, Descent and Galois theory for Hopf categories Blas Torrecillas Jover(University of Almeria.
Caenepeel, Brauer Groups, Hopf Algebras and Galois Theory.K-Monographs in Mathematics (Kluwer, Dordrecht, ) Google ScholarAuthor: Robert G. Underwood. The study of Hopf algebras spans many fields in mathematics including topology, algebraic geometry, algebraic number theory, Galois module theory, cohomology of groups, and formal groups and has wide-ranging connections to fields from theoretical physics to computer science.
The definition of Brauer graph algebras is given in great detail with many examples to illustrate the concepts. An interpretation of Brauer graphs as decorated ribbon graphs is included. A section on gentle algebras and their associated ribbon graph, trivial extensions of gentle algebras Author: Sibylle Schroll.
In , Caenepeel et al. investigated Hopf Galois theory for weak Hopf algebras based on the Galois theory for corings, and in  Wang studied the Morita contexts related to Hopf Galois theory.
Rings, Hopf Algebras, and Brauer Groups 1st Edition. Edited by Stefaan Caenepeel, A Verschoren. CRC Press. topological methods in algebra; an introduction to effective calculus in quantum groups; Kummer theory for monogenic Larson orders; smash (co)products from adjunctions; module-theoretical properties of good curve singularities; Morita.
The deﬁnition of Hopf Galois extension has its roots in the approach of Chase, Harrison and Rosenberg who wanted to generalize the classical Galois theory of automorphism groups of ﬁelds to groups acting on commutative rings.
In Chase and Sweedler extended these ideas to coactions of Hopf algebras acting on a commutative k–algebra,File Size: KB. Included is a systematic development of the theory of Grothendieck topologies and etale cohomology, and discussion of topics such as Gabber's theorem and the theory of Taylor's big Brauer group of algebras without a unit.
Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois. This is the first book to be dedicated entirely to Drinfeld's quasi-Hopf algebras.
Ideal for graduate students and researchers in mathematics and mathematical physics, this treatment is largely self-contained, taking the reader from the basics, with complete proofs, to much more advanced topics, with almost complete : Daniel Bulacu, Stefaan Caenepeel, Florin Panaite, Freddy Van Oystaeyen.
Hopf Algebras and Galois Theory. Stephen U. Chase A-map A*-module abelian group adjointness apply argument arising assume called Chapter coalgebra finitely generated projective flat follows formula functor Furthermore Galois A-object given guarantees hence holds homomorphism Hopf algebra ideal immediate induced inverse isomorphism Lemma.
Hopf Algebras and Quantum Groups - CRC Press Book This volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium. It presents state-of-the-art papers - selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras.
Chapter III. Brauer Group Anthony W. Knapp, Advanced Algebra, Digital Second Edition (East Setauket, NY: Anthony W. Knapp, ), ; Equivariant group cohomology and Brauer group Cegarra, A. and Garzón, A.R., Bulletin of the Belgian Mathematical Society - Simon Stevin, ; Hopf algebroids and Galois extensions Kadison, Lars, Bulletin of the Belgian Mathematical Society - Author: Ehud Meir.
The concept of Hopf algebras was first introduced in the theory of algebraic topology but in recent years has been developed by many mathematicians and applied to other areas of mathematics such as Lie groups, algebraic groups and Galois theory.
This book is an introduction to the basic theory of Hopf algebras for the reader already familiar with the basic ideas of linear algebra and. 1st Edition Published on February 4, by CRC Press. Table of Contents.
Sur les invariants des algebres de Weyl et de leurs corps de fractions; a Picard-Brauer five term exact sequence for braided categories; topological methods in algebra; an introduction to effective calculus in quantum groups; Kummer theory for monogenic Larson orders; smash (co)products from adjunctions; module.
Carnovale / Journal of Algebra () – The case in which V =0 is then dealt with by showing that the Brauer group in this case is the direct product of the Brauer group of k[G] and the group of G-invariant symmetric bilinear forms on V∗.In this.
For many people there is life after 40; for some mathematicians there is algebra after Galois theory. The objective ofthis book is to prove the latter thesis. It is written primarily for students who have assimilated substantial portions of a standard first year graduate algebra textbook, and who have enjoyed the experience.
The material that is presented here should not be fatal if it is. to a unique central division algebra. Brauer group theory has strong connections to Galois theory, Homology theory, Group theory, Algebraic Geometry and K-Theory. Several versions and generalizations of the Brauer group of a eld were proposed through the last century, ending, from a formal point of view, in the construction of the.
Then Hopf–Galois descent theory for linear Hopf categories, the Hopf algebra version of a linear category, is developed. This leads to the notion of Hopf–Galois category extension. We have a dual theory, where actions by dual linear Hopf categories on linear categories are by: 1.
Description: The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups.
It is intended to be a graduate text as well as a research monograph. GALOIS THEORY FOR WEAK HOPF ALGEBRAS S. CAENEPEEL AND E. DE GROOT Abstract. We develop Hopf-Galois theory for weak Hopf algebras, and recover analogs of classical results for Hopf algebras.
Our methods are based on the recently introduced Galois theory for corings. We focus on the situatation where the weak Hopf algebra is a groupoid algebra or. This volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium.
It presents state-of-the-art papers - selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras, including multiplier Hopf algebras and quantum groups.
Rings, Hopf Algebras, and Brauer Groups - CRC Press Book Rings, Hopf Algebras, and Brauer Groups 1st Edition. Stefaan Caenepeel, A Verschoren.
Paperback $ Hardback $ CRC Press Published February 4, Reference - Pages Hopf Algebra: An Introduction. The book features articles by leading researchers on a wide range of themes, specifically, abstract Galois theory, Hopf algebras, and categorical structures, in particular quantum categories and higher-dimensional structures.
Brauer groups, Hopf algebras and Galois theory By Stefaan Caenepeel. Kluwer Academic Publishers, Dordrecht, The Netherlands. pages. $, NLG Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra.
The development of the theory is carried out in such a way that the connection to the theory of the Brauer group in Part I is made clear. Last but not least: In general one can define the Brauer group of a braided monoidal category.
Now let G be a group and ϕ a pairing. One can consider the Hopf algebra KG and using ϕ one can define coquasi-triangular structure on KG. Denote by H the resulting coquasi-triangular Hopf algebra.
Yinhuo Zhang: Braided autoequivalences, quantum commutative Galois objects and the Brauer groups which generalizes the Hopf bi-Galois theory over usual Hopf algebras to. Amazon配送商品ならBrauer Groups, Hopf Algebras and Galois Theory (K-Monographs in Mathematics, Vol 4)が通常配送無料。更にAmazonならポイント還元本が多数。Caenepeel, Stefaan作品ほか、お急ぎ便対象商品は当日お届けも可能。.ﬁnite dimensional Hopf algebra with antipode otherwise stated all tensor products will be over the ﬁeld k.
For general facts on Hopf algebras we refer the reader to  and . The Brauer group, see , : In this paragraph we recall the construction of the Brauer group of a quasitriangular Hopf algebra.
Suppose that R= P.The quantum groups of Drinfeld and Fadeev, as well as quotients of a group by a non-normal subgroup which appear in gauge theory have a paragroup structure. In paragroups the underlying set of a group is replaced by a graph, the group elements are substituted by strings on the graph and a geometrical connection stands for the composition by: