Natural Dualities for the Working Algebraist PDF Download

Author: David M. Clark
Publisher: Cambridge University Press
ISBN: 9780521454155
Category : Mathematics
Languages : en
Pages : 372

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Book Description
First text in subject; aimed at algebraists, category theorists in mathematics and computer science.

Author: Kofi Kissi Dompere
Publisher: Springer Nature
ISBN: 303090279X
Category : Technology & Engineering
Languages : en
Pages : 333

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Book Description
This book is concerned with the development of the understanding of the relational structures of information, knowledge, decision–choice processes of problems and solutions in the theory and practice regarding diversity and unity principles of knowing, science, non-science, and information–knowledge systems through dualistic-polar conditions of variety existence and nonexistence. It is a continuation of the sequence of my epistemic works on the theories on fuzzy rationality, info-statics, info-dynamics, entropy, and their relational connectivity to information, language, knowing, knowledge, cognitive practices relative to variety identification–problem–solution dualities, variety transformation–problem–solution dualities, and variety certainty–uncertainty principle in all areas of knowing and human actions regarding general social transformations. It is also an economic–theoretic approach in understanding the diversity and unity of knowing and science through neuro-decision–choice actions over the space of problem–solution dualities and polarities. The problem–solution dualities are argued to connect all areas of knowing including science and non-science, social science, and non-social-science into unity with diversities under neuro-decision–choice actions to support human existence and nonexistence over the space of static–dynamic dualities. The concepts of diversity and unity are defined and explicated to connect to the tactics and strategies of decision–choice actions over the space of problem–solution dualities. The concepts of problem and solution are defined and explicated not in the space of absoluteness but rather in the space of relativity based on real cost–benefit conditions which are shown to be connected to the general parent–offspring infinite process, where every solution generates new problem(s) which then generates a search for new solutions within the space of minimum–maximum dualities in the decision–choice space under the principle of non-satiation over the space of preference–non-preference dualities with analytical tools drawn from the fuzzy paradigm of thought which connects the conditions of the principle of opposites to the conditions of neuro-decision–choice actions in the zone of variety identifications and transformations. The Monograph would be useful to all areas of Research, Learning and Teaching at Advanced Stages of Knowing and Knowledge Production.

Author: Michelle Voss Roberts
Publisher: Westminster John Knox Press
ISBN: 0664234496
Category : Religion
Languages : en
Pages : 230

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Book Description
Philosophy and theology have each struggled with the problem of dualismùthe conviction that reality comprises material arid nonmaterial entities. Too often, this split places God, spirit, mind, and the masculine in opposition to evil, body, matter, and the feminine. These intellectual divisions support social structures that oppress rather than embrace women, the poor, people of color, and others. With this volume, Voss Roberts expertly shows how comparative theology uproots dualism and fosters new modes of community built on cooperation instead of oppression.

Author: L. Baulieu
Publisher: Springer Science & Business Media
ISBN: 9401147302
Category : Science
Languages : en
Pages : 490

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Book Description
As recent developments have shown, supersymmetric quantum field theory and string theory are intimately related, with advances in one area often shedding light on the other. The organising ideas of most of these advances are the notion of duality and the physics of higher dimensional objects or p-branes. The topics covered in the present volume include duality in field theory, in particular in supersymmetric field theory and supergravity, and in string theory. The Seiberg-Witten theory and its recent developments are also covered in detail. A large fraction of the volume is devoted to the current state of the art in M-theory, in particular its underlying superalgebra as well as its connection with superstring and N = 2 strings. The physics of D-branes and its essential role in the beautiful computation of the black hole entropy is also carefully covered. Finally, the last two sets of lectures are devoted to the exciting matrix approach to non-perturbative string theory.

Author: Shun-Jen Cheng
Publisher: American Mathematical Soc.
ISBN: 0821891189
Category : Mathematics
Languages : en
Pages : 323

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Book Description
This book gives a systematic account of the structure and representation theory of finite-dimensional complex Lie superalgebras of classical type and serves as a good introduction to representation theory of Lie superalgebras. Several folklore results are rigorously proved (and occasionally corrected in detail), sometimes with new proofs. Three important dualities are presented in the book, with the unifying theme of determining irreducible characters of Lie superalgebras. In order of increasing sophistication, they are Schur duality, Howe duality, and super duality. The combinatorics of symmetric functions is developed as needed in connections to Harish-Chandra homomorphism as well as irreducible characters for Lie superalgebras. Schur-Sergeev duality for the queer Lie superalgebra is presented from scratch with complete detail. Howe duality for Lie superalgebras is presented in book form for the first time. Super duality is a new approach developed in the past few years toward understanding the Bernstein-Gelfand-Gelfand category of modules for classical Lie superalgebras. Super duality relates the representation theory of classical Lie superalgebras directly to the representation theory of classical Lie algebras and thus gives a solution to the irreducible character problem of Lie superalgebras via the Kazhdan-Lusztig polynomials of classical Lie algebras.

Author: Jörg Teschner
Publisher: Springer
ISBN: 3319187694
Category : Science
Languages : en
Pages : 467

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Book Description
This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have been studied in this way are partition functions, expectation values of line operators, and supersymmetric indices. The book also reviews recently discovered connections between SUSY field theories in four dimensions and two-dimensional conformal field theory. These connections have a counterpart in relations between three-dimensional gauge theories and Chern-Simons theory; the book’s closing chapters explore connections with string theory.

Author: Michael H. Powell
Publisher: American Mathematical Soc.
ISBN: 9780821818053
Category : Algebraic functions
Languages : en
Pages : 248

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Author: Y M Cho
Publisher: World Scientific
ISBN: 9814531847
Category :
Languages : en
Pages : 408

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Book Description
Contents: Lectures:Supermembranes: An Introduction (M J Duff)An Introduction to p-Branes (K S Stelle)Notes on Matrix Strings and Fivebranes (H Verlinde et al.)Intersecting Branes (J P Gauntlett)BPS Bound States, Supermembranes, and T-Duality in M Theory (J G Russo)D=6, N=1 String Vacua and Duality (L E Ibáñez & A M Uranga)Flat Symplectic Bundles of N-Extended Supergravities, Central Charges and Black-Hole Entropy (S Ferrara et al.)Black Hole Thermodynamics and String Theory (S R Das)Seminars:One-Instanton Calculations in N=2 Supersymmetric Gauge Theories (K Ito)Field Theory on Coadjoint Orbit and Self-Dual Chern-Simons Solitons (P Oh)Cohomological Yang-Mills Theory in Eight Dimensions (H Kanno et al.)Charged BTZ Black Hole as a Global Vortex in Anti-de Sitter Space–Time: A Bridge by Duality (Y Kim et al.)Tensionless Gravitational String in D=6, N=1 Heterotic String Vacua (N Kim et al.)Quantum Ergoregion Instability (G Kang) Readership: High energy physicists. Keywords:

Author: Kitran Macey M. Colwell
Publisher: Springer
ISBN: 3319673920
Category : Science
Languages : en
Pages : 107

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Book Description
This book develops two exciting areas of particle physics research. It applies the recent new insights about the usefulness of helicity amplitudes in understanding gauge theory to the long-standing effort to understand theories with both electric and magnetic charges. It is known that for some supersymmetric theories there is an exact duality that relates two descriptions of the physics, one where the electric charges are weakly coupled and another where the electric charges are strongly coupled. The calculations in this thesis suggest that this duality can also hold in the low-energy limit of nonsupersymmetric gauge theories. The idea of addressing the hierarchy problem of the standard model Higgs mechanism using conformal symmetry is also explored. Analogously to “Little Higgs” models, where divergences are cancelled only at one-loop order, models are studied that have infrared conformal fixed points which related gauge and Yukawa couplings, allowing for a cancellation between seemingly unrelated quantum loop diagrams.

Author: G. Alwyn Zittrauer
Publisher:
ISBN: 9780975949306
Category : Metaphysics
Languages : en
Pages : 0

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