Hopf Monoids And Generalized Permutahedra
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Hopf Monoids And Generalized Permutahedra
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Author : Marcelo Aguiar
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-27
Hopf Monoids And Generalized Permutahedra written by Marcelo Aguiar and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-27 with Mathematics categories.
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Hopf Algebras And Tensor Categories
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Author : Nicolás Andruskiewitsch
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-21
Hopf Algebras And Tensor Categories written by Nicolás Andruskiewitsch 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 2013-02-21 with Mathematics categories.
This volume contains the proceedings of the Conference on Hopf Algebras and Tensor Categories, held July 4-8, 2011, at the University of Almeria, Almeria, Spain. The articles in this volume cover a wide variety of topics related to the theory of Hopf algebras and its connections to other areas of mathematics. In particular, this volume contains a survey covering aspects of the classification of fusion categories using Morita equivalence methods, a long comprehensive introduction to Hopf algebras in the category of species, and a summary of the status to date of the classification of Hopf algebras of dimensions up to 100. Among other topics discussed in this volume are a study of normalized class sum and generalized character table for semisimple Hopf algebras, a contribution to the classification program of finite dimensional pointed Hopf algebras, relations to the conjecture of De Concini, Kac, and Procesi on representations of quantum groups at roots of unity, a categorical approach to the Drinfeld double of a braided Hopf algebra via Hopf monads, an overview of Hom-Hopf algebras, and several discussions on the crossed product construction in different settings.
Monoidal Functors Species And Hopf Algebras
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Author : Marcelo Aguiar
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Monoidal Functors Species And Hopf Algebras written by Marcelo Aguiar 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.
This research monograph integrates ideas from category theory, algebra and combinatorics. It is organized in three parts. Part I belongs to the realm of category theory. It reviews some of the foundational work of Benabou, Eilenberg, Kelly and Mac Lane on monoidal categories and of Joyal and Street on braided monoidal categories, and proceeds to study higher monoidal categories and higher monoidal functors. Special attention is devoted to the notion of a bilax monoidal functor which plays a central role in this work. Combinatorics and geometry are the theme of Part II. Joyal's species constitute a good framework for the study of algebraic structures associated to combinatorial objects. This part discusses the category of species focusing particularly on the Hopf monoids therein. The notion of a Hopf monoid in species parallels that of a Hopf algebra and reflects the manner in which combinatorial structures compose and decompose. Numerous examples of Hopf monoids are given in the text. These are constructed from combinatorial and geometric data and inspired by ideas of Rota and Tits' theory of Coxeter complexes. Part III is of an algebraic nature and shows how ideas in Parts I and II lead to a unified approach to Hopf algebras. The main step is the construction of Fock functors from species to graded vector spaces. 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. It is written with clarity and sufficient detail to make it accessible to advanced graduate students.
Bimonoids For Hyperplane Arrangements
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Author : Marcelo Aguiar
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-19
Bimonoids For Hyperplane Arrangements written by Marcelo Aguiar 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 2020-03-19 with Mathematics categories.
The goal of this monograph is to develop Hopf theory in a new setting which features centrally a real hyperplane arrangement. The new theory is parallel to the classical theory of connected Hopf algebras, and relates to it when specialized to the braid arrangement. Joyal's theory of combinatorial species, ideas from Tits' theory of buildings, and Rota's work on incidence algebras inspire and find a common expression in this theory. The authors introduce notions of monoid, comonoid, bimonoid, and Lie monoid relative to a fixed hyperplane arrangement. They also construct universal bimonoids by using generalizations of the classical notions of shuffle and quasishuffle, and establish the Borel-Hopf, Poincar -Birkhoff-Witt, and Cartier-Milnor-Moore theorems in this setting. This monograph opens a vast new area of research. It will be of interest to students and researchers working in the areas of hyperplane arrangements, semigroup theory, Hopf algebras, algebraic Lie theory, operads, and category theory.
Roads To Higher Dimensional Polytopic Projects
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Author : Octavian Iordache
language : en
Publisher: Springer Nature
Release Date : 2022-08-18
Roads To Higher Dimensional Polytopic Projects written by Octavian Iordache and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-18 with Technology & Engineering categories.
High dimensional reference architectures presented here allows confronting and prevailing over the growing complexity of polytopic projects implementations. Such projects should be envisaged giving that conventional systems operations, equipments, methodologies or organizations will reach their limits for self-evolvability in high complexity conditions. Self-evolvable high complexity systems are based on high dimensional polytopic reference architectures. Polytope is the general term of the sequence: point, line, polygon, polyhedron and so on.The polytopic projects are targeting the artificiality, not only for materials where it is well known and applied, but also for biological, cognitive, intelligent and mathematical systems. The book highlights the polytopic projects basic similarity despite the noticeable difference as domains of application. The roads to follow and the algebra of changing roads are emphasized. The book is divided in 9 chapters. Chapter 1 introduces the Polytopic Roadmap to 4D and beyond. The role for the dialogue of processes in duality of the non-Aristotelian Logic of Contradiction and of Included Middle is emphasized for different domains. Chapter 2 refers to chemical systems. Supramolecular chemistry, metal organic frameworks, MOF, and reaction networks, are the examples considered in the frame of polytopic chemistry. Chapter 3 refers to biological systems. Biological dynamical hierarchies and quasi-species are the considered case studies. Technological and scientific projects targeting artificiality for cells and viruses are considered. Chapter 4 refers to cognitive systems. Developmental stages, formal and relational concepts analysis, and neural coding are considered here. The roles of the 4D systems of systems of systems and of conceptual 4D-cube are emphasized. Artificiality for cognitive systems is the object of study. Chapter 5 refers to mathematical systems. Modeling levels and the 4D digital twins are discussed. Hopf monoids as tools for the study of combinations and separations, dual graded graphs and V-models are informally presented. Chapter 6 refers to application of formal concept analysis, FCA, for high dimensional separations, nesting and drug delivery. Chapter 7 refers to polytopic engineering systems as multiscale transfer, distributors-collectors, cyclic operations, middle vessel columns, mixing, assembly and designs. Equipments have been characterized using Polytopic Roadmaps and classified by Periodic Tables. Chapter 8 introduces polytopic industry, economy, society and sustainability. Chapter 9 outlines new domains of interest as arts and architecture, transdisciplinarity, complex systems and unity of sciences and engineering. Polytopic Roadmaps are proposed as Method for experts from various fields to synthesize their thinking and capabilities into new projects implementation to face and surpass high complexity. A repetitive finding of this book is that self-evolvability observed in physical systems is based on the same directed sequence of reference architectures as the self-evolvability of concepts in our mind. Continuing to develop the field of self-evolvable systems and presenting the polytopic roadmaps for 4D and beyond advances in ever growing complexity domains, the book will be useful to engineers, researchers, entrepreneurs and students in different branches of production, complex systems sciences and engineering, ecology and applied mathematics.
Handbook Of The Tutte Polynomial And Related Topics
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Author : Joanna A. Ellis-Monaghan
language : en
Publisher: CRC Press
Release Date : 2022-07-06
Handbook Of The Tutte Polynomial And Related Topics written by Joanna A. Ellis-Monaghan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-06 with Computers categories.
The Tutte Polynomial touches on nearly every area of combinatorics as well as many other fields, including statistical mechanics, coding theory, and DNA sequencing. It is one of the most studied graph polynomials. Handbook of the Tutte Polynomial and Related Topics is the first handbook published on the Tutte Polynomial. It consists of thirty-four chapters written by experts in the field, which collectively offer a concise overview of the polynomial’s many properties and applications. Each chapter covers a different aspect of the Tutte polynomial and contains the central results and references for its topic. The chapters are organized into six parts. Part I describes the fundamental properties of the Tutte polynomial, providing an overview of the Tutte polynomial and the necessary background for the rest of the handbook. Part II is concerned with questions of computation, complexity, and approximation for the Tutte polynomial; Part III covers a selection of related graph polynomials; Part IV discusses a range of applications of the Tutte polynomial to mathematics, physics, and biology; Part V includes various extensions and generalizations of the Tutte polynomial; and Part VI provides a history of the development of the Tutte polynomial. Features Written in an accessible style for non-experts, yet extensive enough for experts Serves as a comprehensive and accessible introduction to the theory of graph polynomials for researchers in mathematics, physics, and computer science Provides an extensive reference volume for the evaluations, theorems, and properties of the Tutte polynomial and related graph, matroid, and knot invariants Offers broad coverage, touching on the wide range of applications of the Tutte polynomial and its various specializations
The Space Of Spaces Curvature Bounds And Gradient Flows On The Space Of Metric Measure Spaces
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Author : Karl-Theodor Sturm
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-27
The Space Of Spaces Curvature Bounds And Gradient Flows On The Space Of Metric Measure Spaces written by Karl-Theodor Sturm and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-27 with Mathematics categories.
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Sur Un Probl Me De Compatibilit Local Global Localement Analytique
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Author : Christophe Breuil
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-27
Sur Un Probl Me De Compatibilit Local Global Localement Analytique written by Christophe Breuil and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-27 with Mathematics categories.
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Potential Estimates And Quasilinear Parabolic Equations With Measure Data
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Author : Quoc-Hung Nguyen
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-19
Potential Estimates And Quasilinear Parabolic Equations With Measure Data written by Quoc-Hung Nguyen and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-19 with Mathematics categories.
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On The Boundary Behavior Of Mass Minimizing Integral Currents
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Author : Camillo De Lellis
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-17
On The Boundary Behavior Of Mass Minimizing Integral Currents written by Camillo De Lellis and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-17 with Mathematics categories.
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