Kac Algebras Arising From Composition Of Subfactors General Theory And Classification
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Kac Algebras Arising From Composition Of Subfactors General Theory And Classification
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Author : Masaki Izumi
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Kac Algebras Arising From Composition Of Subfactors General Theory And Classification written by Masaki Izumi 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 2002 with Mathematics categories.
This title deals with a map $\alpha$ from a finite group $G$ into the automorphism group $Aut({\mathcal L})$ of a factor ${\mathcal L}$ satisfying (i) $G=N \rtimes H$ is a semi-direct product, (ii) the induced map $g \in G \to [\alpha_g] \in Out({\mathcal L})=Aut({\mathcal L})/Int({\mathcal L})$ is an injective homomorphism, and (iii) the restrictions $\alpha \! \! \mid_N, \alpha \! \! \mid_H$ are genuine actions of the subgroups on the factor ${\mathcal L}$. The pair ${\mathcal M}={\mathcal L} \rtimes_{\alpha} H \supseteq {\mathcal N}={\mathcal L} DEGREES{\alpha\mid_N}$ (of the crossed product ${\mathcal L} \rtimes_{\alpha} H$ and the fixed-point algebra ${\mathcal L} DEGREES{\alpha\mid_N}$) gives an irreducible inclusion of factors with Jones index $\# G$. The inclusion ${\mathcal M} \supseteq {\mathcal N}$ is of depth $2$ and hence known to correspond to a Kac algebra of dim
Classification Of Actions Of Discrete Kac Algebras On Injective Factors
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Author : Toshihiko Masuda
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-01-18
Classification Of Actions Of Discrete Kac Algebras On Injective Factors written by Toshihiko Masuda 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 2017-01-18 with Mathematics categories.
The authors study two kinds of actions of a discrete amenable Kac algebra. The first one is an action whose modular part is normal. They construct a new invariant which generalizes a characteristic invariant for a discrete group action, and we will present a complete classification. The second is a centrally free action. By constructing a Rohlin tower in an asymptotic centralizer, the authors show that the Connes–Takesaki module is a complete invariant.
Kac Algebras Arising From Composition Of Subfactors
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Author : Masaki Izumi
language : en
Publisher:
Release Date : 2014-09-11
Kac Algebras Arising From Composition Of Subfactors written by Masaki Izumi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with MATHEMATICS categories.
This title deals with a map $\alpha$ from a finite group $G$ into the automorphism group $Aut({\mathcal L})$ of a factor ${\mathcal L}$ satisfying (i) $G=N \rtimes H$ is a semi-direct product, (ii) the induced map $g \in G \to [\alpha_g] \in Out({\mathcal L})=Aut({\mathcal L})/Int({\mathcal L})$ is an injective homomorphism, and (iii) the restrictions $\alpha \! \! \mid_N, \alpha \! \! \mid_H$ are genuine actions of the subgroups on the factor ${\mathcal L}$. The pair ${\mathcal M}={\mathcal L} \rtimes_{\alpha} H \supseteq {\mathcal N}={\mathcal L} DEGREES{\alpha\mid_N}$ (of the crossed product ${\mathcal L} \rtimes_{\alpha} H$ and the fixed-point algebra ${\mathcal L} DEGREES{\alpha\mid_N}$) gives an irreducible inclusion of factors with Jones index $\# G$. The inclusion ${\mathcal M} \supseteq {\mathcal N}$ is of depth $2$ and hence known to correspond to a Kac algebra of dim
New Directions In Hopf Algebras
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Author : Susan Montgomery
language : en
Publisher: Cambridge University Press
Release Date : 2002-05-06
New Directions In Hopf Algebras written by Susan Montgomery 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 2002-05-06 with Mathematics categories.
Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras and other areas of physics and mathematics. They have been intensely studied in the past; in particular, the solution of a number of conjectures of Kaplansky from the 1970s has led to progress on the classification of semisimple Hopf algebras and on the structure of pointed Hopf algebras. Among the topics covered are results toward the classification of finite-dimensional Hopf algebras (semisimple and non-semisimple), as well as what is known about the extension theory of Hopf algebras. Some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to work in quantum groups. The book also explores the connections and applications of Hopf algebras to other fields.
Semisolvability Of Semisimple Hopf Algebras Of Low Dimension
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Author : Sonia Natale
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Semisolvability Of Semisimple Hopf Algebras Of Low Dimension written by Sonia Natale 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 2007 with Mathematics categories.
The author proves that every semisimple Hopf algebra of dimension less than $60$ over an algebraically closed field $k$ of characteristic zero is either upper or lower semisolvable up to a cocycle twist.
Derived Ell Adic Categories For Algebraic Stacks
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Author : Kai Behrend
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Derived Ell Adic Categories For Algebraic Stacks written by Kai Behrend 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 2003 with Mathematics categories.
This text is intended for graduate students and research mathematicians interested in algebraic geometry, category theory and homological algebra.
On The Classification Of Polish Metric Spaces Up To Isometry
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Author : Su Gao
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
On The Classification Of Polish Metric Spaces Up To Isometry written by Su Gao 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 2003 with Mathematics categories.
Classification And Probabilistic Representation Of The Positive Solutions Of A Semilinear Elliptic Equation
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Author : Benoît Mselati
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Classification And Probabilistic Representation Of The Positive Solutions Of A Semilinear Elliptic Equation written by Benoît Mselati 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 2004 with Mathematics categories.
Concerned with the nonnegative solutions of $\Delta u = u^2$ in a bounded and smooth domain in $\mathbb{R}^d$, this title intends to prove that they are uniquely determined by their fine trace on the boundary as defined in [DK98a], answering a major open question of [Dy02].
The Role Of The Spectrum In The Cyclic Behavior Of Composition Operators
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Author : Eva A. Gallardo-Gutieŕrez
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
The Role Of The Spectrum In The Cyclic Behavior Of Composition Operators written by Eva A. Gallardo-Gutieŕrez 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 2004 with Mathematics categories.
Introduction and preliminaries Linear fractional maps with an interior fixed point Non elliptic automorphisms The parabolic non automorphism Supercyclic linear fractional composition operators Endnotes Bibliography.
Groups Rings Lie And Hopf Algebras
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Author : Y. Bahturin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Groups Rings Lie And Hopf Algebras written by Y. Bahturin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.