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Thursday, April 30, 2020 | History

2 edition of Modular invariants. found in the catalog.

Modular invariants.

Daniel Edwin Rutherford

Modular invariants.

  • 351 Want to read
  • 33 Currently reading

Published by University Press in Cambridge .
Written in English

    Subjects:
  • Invariants

  • Edition Notes

    SeriesCambridge tracts in mathematics and mathematical physics, no. 27
    The Physical Object
    Pagination84p.
    Number of Pages84
    ID Numbers
    Open LibraryOL14808602M

    We reconstruct invariants of Mumford curves related to valuations of generators of the associated Schottky group, by developing a graphical theory for KMS weights on the associated graph C∗-algebra, and using modular index theory for KMS weights. We give explicit examples of the construction of graph weights for low genus Mumford curves.


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Modular invariants. by Daniel Edwin Rutherford Download PDF EPUB FB2

Buy Modular Invariants on FREE SHIPPING on qualified orders Modular Invariants: D.E Rutherford: : Books Skip to main content. This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group.

It explains a theory that is more complicated than the study of the classical non-modular case, and it describes many open by: This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case.

Largely self-contained, the book develops the theory from its origins up. Modular Invariant Theory H.E.A. Eddy Campbell, David L.

Wehlau (auth.) This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group. It explains a theory that is more complicated than the study of the classical non-modular case, and it describes many open questions.

“The main aim of the book is to give an account of Hida’s results on arithmetic invariants in an accessible way. The book is intended for mathematicians with some background on modular forms and is worthwhile for both graduate students and experts. Cited by: Introduction This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group.

It explains a theory that is more complicated than Modular invariants. book study of the classical non-modular case, and it describes many open questions. I have a better modern book on invariant theory:Classical Invariant Theory (London Mathematical Society Student Texts),but in modular group theory wasn't as set in in the way it was presented, so when he talks of SL(2,p) modular groups, he never gives the reference.

The cross applications to Lie groups, graph theory and combinatorial analysisCited by: “The main aim of the book is to give an account of Hida’s results on arithmetic invariants in an accessible way.

The book is intended for mathematicians with some background on modular forms and is worthwhile for both graduate students and experts. Brand: Springer-Verlag New York. Rutherford's dissertation was published in as Modular Invariants in the Cambridge Tracts.

In mathematics, Felix Klein's j-invariant or j function, regarded as a function of a complex variable τ, is a modular function of weight zero for SL(2, Z) defined on the upper half-plane of complex is the unique such function which is holomorphic away from a simple pole at the cusp such that (/) =.

Rational functions of j are modular, and in fact give all modular functions. Invariants are used in diverse areas of mathematics such as geometry, topology, algebra and discrete mathematics. Some important classes of transformations are defined by an invariant they leave unchanged. For example, conformal maps are defined as transformations of the plane that preserve angles.

The discovery of invariants is an important. Genre/Form: Modulare Invariantentheorie: Additional Physical Format: Online version: Rutherford, D.E. (Daniel Edwin), Modular invariants. Cambridge [Eng.

] L. DICKSON: MODULAR INVARIANTS Absolute and relative invariants of a system of forms. When L is the group G of all m-ary linear homogeneous transformations in the GF\\p*~\, the invariants defined in §§3, 4 are called the absolute invariants of the s forms.

When L is the group Gx of all transformations ofFile Size: 2MB. Eric Temple Bell wrote, "Miss Sanderson's single contribution () to modular invariants has been rated by competent judges as one of the classics of the subject." [1] A Mildred L.

Sanderson prize for excellence in mathematics was established in her honor in at Mount Holyoke :Waltham, Massachusetts, US. Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles.

The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and.

This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including μ-invariant, L-invariant, and similar book can be regarded as an introductory text to the author's previous book p-Adic Automorphic Forms on Shimura n as a down-to-earth introduction to Shimura varieties, this text includes many.

3 Modular Invariants and the Classification of von Neumann Algebras As previously mentioned, the modular structure carries information about the algebra.

This is best evidenced in the structure of type III factors. As this theory is rather involved, only a sketch of some of the results can be given. Reflection groups and their invariant theory provide the main themes of this book and the first two parts focus on these topics.

The first 13 chapters deal with reflection groups (Coxeter groups and Weyl groups) in Euclidean Space while the next thirteen chapters study the invariant theory of pseudo-reflection groups. The third part of the book studies conjugacy classes of the elements in.

This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case.

Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the.

Invariants and Relative Invariants 2. Finite Generation of Invariants 3. Construction of Invariants 4. Poincare Series 5. Dimension Theoretic Properties of Rings of Invariants 6. Homological Properties of Invariants 7. Groups Generated by Reflections 8. Modular Invariants 9. Modular invariant theory.

[H E A Eddy Campbell; David L Wehlau] -- "This book covers the modular invariant theory of finite groups, the case when the characteristic. From the table of contents: Invariants and Relative Invariants - Finite Generation of Invariants - Construction of Invariants - Poincaré Series - Dimension Theoretic Properties of Rings of Invariants - Homological Properties of Invariants - Groups Generated by Reflections - Modular Invariants - Polynomial Tensor Exterior Algebras - Invariant Cited by: Abstract.

In this chapter, we discuss the modular case of invariant theory. We proved in Chapter 18 that, in the nonmodular case, a finite group G ⊂ GL(V) is a pseudo-reflection group if and only if the ring of invariants S(V) G is a polynomial algebra.

This result is only partly true in the modular : Richard Kane, Jonathan Borwein, Peter Borwein. Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles.

The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras.

The many exercises, with a wide spectrum of difficulty and subjects. Given the list o f all modular invariants of a S-and T-model, it is an interesting problem to determine which ones can be produced by braided subfac- tors through α -induction.

This book covers the modular invariant theory of finite groups. It details techniques for the computation of invariants for many modular representations of finite groups, especially the cyclic group of prime order, and includes many examples.

Modular invariants satisfy remarkable fusion rules. Let Z be a modular invariant associated to a braided subfactor N ⊂ M. The decomposition of the non-normalized modular invariants ZZ* and Z*Z into sums of normalized modular invariants is related to the decomposition of the full Cited by: Audio Books & Poetry Computers, Technology and Science Music, Arts & Culture News & Public Affairs Non-English Audio Spirituality & Religion Build Your Business (Mindset & Success) Librivox Free Audiobook.

Full text of "Modular Invariants" See other formats. Volumenumber 1,2 PHYSICS LETTERS B 12 February MODULAR INVARIANT PARTITION FUNCTIONS OF SUPERCONFORMAL THEORIES A. CAPPELLI 1 Service de Physique Thrique, CEN-Saclay, Gif-sur-Yvette Cedex, France Received 29 October The modular invariant partition functions of two-dimensional minimal superconformal theories are obtained by extending a systematic Cited by: In mathematics, a modular invariant of a group is an invariant of a finite group acting on a vector space of positive characteristic (usually dividing the order of the group).

The study of modular invariants was originated in about by Dickson (). Dickson invariant [ edit ]. Modular Invariants for Layered Object Structures Peter Muller ¨ Arnd Poetzsch-Heffter Gary T.

Leavens ETH Zurich Technische Universitat ¨ Iowa State University, Department of Computer Kaiserslautern, Germany Ames, Iowa, USA Science [email protected] ETH Zentrum, RZ J9 poetzsch CH Zurich, Switzerland @ [email protected] ABSTRACT sound for invariants.

We discuss the modular invariance of the SL(2,R) WZW particular, we discuss in detail the modular invariants using the sl ̂ (2,R) characters based on the discrete unitary series of the SL(2,R) explicit forms of the corresponding characters are Cited by: Addeddate Call number Digitalpublicationdate /04/30 Identifier modularinvariantmbp Identifier-ark ark://t89g5hj2v.

Springer, 3 books Mara D. Neusel, 3 books Jan Flusser, 3 books Hanspeter Kraft, 2 books A. Verschoren, 2 books Leonard E. Dickson, 2 books Peter Slodowy, 2 books Issai Schur, 2 books David Hilbert, 2 books G.

Gurevich, 2 books Harold Hilton, 2 books Peter J. Olver, 2 books S. Koh, 2 books Roe Goodman, 2 books David Mumford, 2 books. Consider a finite dimensional vector space V over a finite field F give a minimal generating set for the ring of invariants F q [V ⊕ V ⁎] GL (V), and show that this ring is a Gorenstein ring but is not a complete results confirm a conjecture of Bonnafé and Kemper [3, Conjecture ].Cited by: A modular invariant of a group acting on a vector space of positive characteristic The elliptic modular function, giving the modular invariant of an elliptic curve.

Disambiguation page providing links to topics that could be referred to by the same search term This disambiguation page lists mathematics articles associated with the same title. Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition.

The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory.

A modular invariant for a chiral conformal field theory is physical if there is a full conformal field theory with the given chiral halves realising the modular invariant.

The easiest modular invariants are the charge conjugation and the diagonal modular invariants. Moonshine Beyond the Monster describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory Cited by: Classical specification and verification techniques support invariants for individual objects whose fields are primitive values, but do not allow sound modular reasoning about invariants involving more complex object structures.

Such non-trivial object structures are common, and occur in lists, hash tables, and whenever systems are built in by:. Modular Invariant Theory by H.

E. A. Eddy Campbell,available at Book Depository with free delivery worldwide.We study modular invariants of finite affine linear groups over a finite field \(\mathbb {F}_{q}\) under affine actions and linear actions.

We generalize a result of Chuai (J Algebra – Author: Yin Chen.the type analysis and associated type invariants, leading to ineffi-cient analysis and verbose specifications.

In contrast, we propose a generic lifting of modular refinement type analyses with a symbolic analysis to efficiently and effectively check concise invariants that hold almost everywhere. The result is an efficient, highly modular.