Hopf Algebras And Their Actions On Rings
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Hopf Algebras And Their Actions On Rings
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Author : Susan Montgomery
language : en
Publisher: American Mathematical Soc.
Release Date : 1993-10-28
Hopf Algebras And Their Actions On Rings written by Susan Montgomery and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-28 with Mathematics categories.
The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.
Rings Hopf Algebras And Brauer Groups
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Author : Stefaan Caenepeel
language : en
Publisher: CRC Press
Release Date : 2020-09-30
Rings Hopf Algebras And Brauer Groups written by Stefaan Caenepeel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-30 with Mathematics categories.
"Based on papers presented at a recent international conference on algebra and algebraic geometry held jointly in Antwerp and Brussels, Belgium. Presents both survey and research articles featuring new results from the intersection of algebra and geometry. "
Algebras Rings And Modules
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Author : Michiel Hazewinkel
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Algebras Rings And Modules written by Michiel Hazewinkel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Presenting an introduction to the theory of Hopf algebras, the authors also discuss some important aspects of the theory of Lie algebras. This book includes a chapters on the Hopf algebra of symmetric functions, the Hopf algebra of representations of the symmetric groups, the Hopf algebras of the nonsymmetric and quasisymmetric functions, and the Hopf algebra of permutations.
Group Actions On Rings
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Author : Susan Montgomery
language : en
Publisher: American Mathematical Soc.
Release Date : 1985
Group Actions On Rings written by Susan Montgomery and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
Ring theorists and researchers in invariant theory and operator algebra met at Bowdoin for the 1984 AMS-IMS-SIAM Joint Summer Research Conference to exchange ideas about group actions on rings. This work discusses topics common to the three fields, including: $K$-theory, dual actions, semi-invariants and crossed products.
Groups Rings Group Rings And Hopf Algebras
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Author : Jeffrey Bergen
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-24
Groups Rings Group Rings And Hopf Algebras written by Jeffrey Bergen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-24 with Associative rings and algebras -- Modules, bimodules and ideals -- Modules, bimodules and ideals categories.
This volume contains the proceedings of the International Conference on Groups, Rings, Group Rings, and Hopf Algebras, held October 2–4, 2015 at Loyola University, Chicago, IL, and the AMS Special Session on Groups, Rings, Group Rings, and Hopf Algebras, held October 3–4, 2015, at Loyola University, Chicago, IL. Both conferences were held in honor of Donald S. Passman's 75th Birthday. Centered in the area of group rings and algebras, this volume contains a mixture of cutting edge research topics in group theory, ring theory, algebras and their representations, Hopf algebras and quantum groups.
Taming Wild Extensions Hopf Algebras And Local Galois Module Theory
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Author : Lindsay Childs
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Taming Wild Extensions Hopf Algebras And Local Galois Module Theory written by Lindsay Childs and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results, not previously published in book form, show that Hopf algebras play a natural role in local Galois module theory. Included in this work are expositions of short exact sequences of Hopf algebras; Hopf Galois structures on separable field extensions; a generalization of Noether's theorem on the Galois module structure of tamely ramified extensions of local fields to wild extensions acted on by Hopf algebras; connections between tameness and being Galois for algebras acted on by a Hopf algebra; constructions by Larson and Greither of Hopf orders over valuation rings; ramification criteria of Byott and Greither for the associated order of the valuation ring of an extension of local fields to be Hopf order; the Galois module structure of wildly ramified cyclic extensions of local fields of degree p and p2; and Kummer theory of formal groups. Beyond a general background in graduate-level algebra, some chapters assume an acquaintance with some algebraic number theory. From there, this exposition serves as an excellent resource and motivation for further work in the field.
Hopf Algebras And Their Generalizations From A Category Theoretical Point Of View
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Author : Gabriella Böhm
language : en
Publisher: Springer
Release Date : 2018-11-01
Hopf Algebras And Their Generalizations From A Category Theoretical Point Of View written by Gabriella Böhm and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-01 with Mathematics categories.
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.
Quasi Hopf Algebras
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Author : Daniel Bulacu
language : en
Publisher: Cambridge University Press
Release Date : 2019-02-21
Quasi Hopf Algebras written by Daniel Bulacu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-21 with Mathematics categories.
This self-contained book dedicated to Drinfeld's quasi-Hopf algebras takes the reader from the basics to the state of the art.
Algebras Rings And Modules
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Author : Michiel Hazewinkel
language : en
Publisher: CRC Press
Release Date : 2016-04-05
Algebras Rings And Modules written by Michiel Hazewinkel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-05 with Mathematics categories.
The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other volumes. The relevant constructions and results from earlier volumes have been presented in this volume.
Hopf Algebras Polynomial Formal Groups And Raynaud Orders
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Author : Lindsay Childs
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Hopf Algebras Polynomial Formal Groups And Raynaud Orders written by Lindsay Childs and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This volume gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose invariants satisfy a certain $p$-adic condition.