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Thursday, July 30, 2020 | History

4 edition of Non-Abelian cohomology theory and applications to the Yang-Mills & Bäcklund problems found in the catalog.

Non-Abelian cohomology theory and applications to the Yang-Mills & Bäcklund problems

S. I. Andersson

Non-Abelian cohomology theory and applications to the Yang-Mills & Bäcklund problems

by S. I. Andersson

  • 131 Want to read
  • 3 Currently reading

Published by World Scientific in Singapore, New Jersey .
Written in English

    Subjects:
  • Yang-Mills theory,
  • Cohomology theory,
  • Non-Abelian groups,
  • Mathematical physics

  • Edition Notes

    Includes bibliographical references.

    StatementStig I. Andersson.
    Classifications
    LC ClassificationsQC174.52.Y37 A53 1994
    The Physical Object
    Paginationp. cm.
    ID Numbers
    Open LibraryOL1109994M
    ISBN 109971500132
    LC Control Number94035407

    One small remark: Motivic cohomology is usually thought of as the universal Bloch-Ogus cohomology, while the universal Weil cohomology should probably be pure motives with respect to rational equivalence ("probably", because it depends on what exactly you mean by "universal" and "Weil cohomology"). The two notions are closely related though. and cohomology theory of groups, with an emphasis on infinite groups and finiteness properties. The lectures are based on my book [3] and are organized as follows: 1. In the first lecture we will redefine H∗(G) for an arbitrary group G, taking the algebraic point of view (homological algebra) that had evolved by the end of the s.

    0. Introduction. Algebraic homology and cohomology theory may be consid-ered an extension of ordinary representation theory. Certain problems of the latter discipline initially motivated the definition of low-dimensional cohomology groups which subsequently was generalized to arbitrary dimension (cf. [2, 8]). The theory. Whereas usual Hodge theory concerns mainly the usual or abelian cohomology of an algebraic variety—or eventually the rational homotopy theory or nilpotent completion of π 1 which are in some sense obtained by extensions—nonabelian Hodge theory con-cerns the cohomology of a variety with nonabelian coefficients. Because of the basic fact.

    Crossed Modules and H3 (Sketch) -- 6. Extensions With Non-Abelian Kernel (Sketch) -- V Products -- 1. The Tensor Product of Resolutions -- 2. Cross-products -- 3. Cup and Cap Products -- 4. Composition Products -- 5. The Pontryagin Product -- 6. Application: Calculation of the Homology of an Abelian Group -- VI Cohomology Theory of Finite. See e.g. [Sch13, Hol08a,DHI04] for the technical background on (∞-)stacks and [BSS18] for a physical example given by the stack of non-Abelian Yang-Mills fields. It is important to emphasize.


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Non-Abelian cohomology theory and applications to the Yang-Mills & Bäcklund problems by S. I. Andersson Download PDF EPUB FB2

Abstract. In the first section some functorial propeties of the non-abelian tensor product of groups are established. With the use of the non-abelian left derived functors [44,62] the homology groups of groups are constructed with coefficients in any group, as the left derived functors of the non-abelian tensor product, which generalize the classical theory of homology of : Hvedri Inassaridze.

Dedecker P. () Three dimensional non-abelian cohomology for groups. In: Category Theory, Homology Theory and their Applications II. Lecture Notes in Mathematics, vol Cited by: This book provides an introduction to the cohomology theory of Lie groups and Lie algebras and to some of its applications in physics.

The mathematical topics covered include the differential. Non-abelian Cohomology and Rational Points - Volume Issue 3 - David Harari, Alexei N. SkorobogatovCited by:   In this chapter we study a general technique to deal with such gluing problems – at least if the difference of two possible local objects is given by a sheaf of groups.

For instance two primitives of a \(\mathbb{K}\) -valued function always differ by a locally constant \(\mathbb{K}\) -valued function and these form a sheaf of groups.

o: TWO-DIMENSIONAL COHOMOLOGY AND SPECTRAL SEQUENCES IN NON-ABELIAN THEORY. in "Questions in group theory and homological algebra". Jaroslavl p. – (russian). This section gives some basic definitions on Abelian and non-Abelian Hodge theory which will be used in the paper later.

For details on them consult the sources indicated below. Hodge-De Rham theory. Fix a smooth complex algebraic variety M. There are various cohomology theories which associate a graded anti-commutative ring to the variety M.

In particular, we develop a cohomology theory which measures the existence of connections and curvings for G-gerbes over stacks. We also introduce G-central extensions of groupoids, generalizing. Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics.

No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail). As a second year graduate textbook, Cohomology of Groups introduces students to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites.

No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology. In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain logy can be viewed as a method of assigning richer algebraic invariants to a space than homology.

Some versions of cohomology arise by dualizing the construction of homology. An application to classifying theory for fiberwise principal bundles is described. between continuous and smooth non-abelian cohomology, and an explicit equivalence between bundle gerbes and.

for the general case, we show that the obstruction of the existence of a non-abelian extension is given by an element in the third cohomology group. The paper is or ganized as follows.

In mathematics (more specifically, in homological algebra), group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic ous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of the group.

By treating the G-module as a kind of. As a second year graduate textbook, Cohomology of Groups introduces students to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites.

No homological algebra is assumed beyond what is normally learned in. Another (not unrelated) reason that cohomology can be easier to work with is that cohomology is a representable functor: H^n(X;A) is homotopy classes of maps from X to the Eilenberg-MacLane space K(A,n).

By Yoneda, this means many properties of cohomology can be computed and understood by computing a single universal example. MO is a rather weak cobordism theory, as the spectrum MO is isomorphic to H(π * (MO)) ("homology with coefficients in π * (MO)") – MO is a product of Eilenberg–MacLane spectra.

In other words, the corresponding homology and cohomology theories are no more powerful than homology and cohomology with coefficients in Z/2Z.

This was the first. homology and cohomology theory is provided in addition. The 1-st cohomology group generators have been shown to be useful also to couple the geometric A-c formulation with electric circuits, see [Dłotko, Specogna, and Trevisan ()].

Hence, the techniques presented in. I learned sheaf cohomology from Claire Voisin's Hodge Theory and Complex Algebraic Geometry I. This is a great book. As its name suggests, it also spends quite some time explaining Dolbeault cohomology, De Rham cohomology, singular cohomology, and how all these are defined/can be understood in terms of sheaf cohomology.

Preface The concepts and methods of topology and geometry are an indispensable part of theoretical physics today. They have led to a deeper understanding of many. of non-abelian electric and magnetic fields is practically ab-sent [6–9].

The main goal of this paper is to present some classical properties for non-abelian Yang-Mills theories. We can ex-tract these properties writing the equation of motion for non-abelian Yang-Mills theories using the language of electric and magnetic fields.object Cin C a C-valued coarse cohomology theory Q C.

For the category of spectra C = Sp and for the sphere spectrum C= Swe obtain a coarse version Q S of stable cohomotopy. 3. If Eis a C-valued coarse homology theory and Cis an object of C, then in the De nition we de ne the dual Sp-valued coarse cohomology theory D C(E) by.this fact. In the mid-eighties some important steps were made in the theory of Gr obner bases in non-commutative rings, notably in rings of di erential operators.

This chapter is about some of the applications of this theory to problems in commutative algebra and algebraic geometry. Our interest in rings of di erential operators and D-modules.