Lie Theory and Its Applications in Physics: Varna, Bulgaria, June 2015

ISBN-13: 9789811026355 / Angielski / Twarda / 2016 / 614 str.

Vladimir Dobrev

Spis treści

Luigi Accardi, Abdessatar Barhoumi, Yun Gang Lu, and

Mohamed Rhaima: *–Lie Algebras Canonically Associated to Probability Measures on R with All Moments.- Loriano Bonora: Special Conformal Transformations and Contact Terms.- Ivan Dimitrijevic, Branko Dragovich, Jelena Stankovic, Alexey S. Koshelev, and Zoran Rakic: On Nonlocal Modified Gravity and Its Cosmological Solutions.- Malte Henkel: Kinetics of Interface Growth: Physical Ageing and Dynamical Symmetries.- Evgeny Ivanov and Stepan Sidorov: News on SU(2|1) Supersymmetric Mechanics.- Toshiyuki Kobayashi: Intrinsic Sound of Anti-de Sitter Manifolds.- Efrat Gerchkovitz and Zohar Komargodski: Sphere Partition Functions and the Kahler Metric on the Conformal Manifold.- Mikhail V. Ignatyev, Ivan Penkov, and Joseph A. Wolf: Real Group Orbits on Flag Ind-Varieties of SL(∞,C).- Raul Gomez and Birgit Speh: Derived functors and Intertwining operators for Principal Series Representations of SL2(R).- Ivan Todorov: Hyperlogarithms and Periods in Feynman Amplitudes.- N.I. Stoilova and J. Van der Jeugt: The Parastatistics Fock Space and Explicit Infinite-Dimensional Representations of the Lie Superalgebra osp(2m+1|2n).- Joseph A. Wolf: Stepwise Square Integrable Representations: the Concept and Some Consequences.- G. Manolakos and G. Zoupanos: Higher-Dimensional Unified Theories with Continuous and Fuzzy Coset Spaces as Extra Dimensions.- Fumihiko Sugino: Higher Genus Amplitudes in SUSY Double-Well Matrix Model for 2D IIA Superstring.- Eduardo Guendelman, Emil Nissimov, Svetlana Pacheva, and Michail Stoilov: Kruskal-Penrose Formalism for Lightlike Thin-Shell Wormholes.- Eduardo Guendelman, Emil Nissimov, and Svetlana Pacheva: Metric-Independent Spacetime Volume-Forms and Dark Energy/Dark Matter Unification.- Hervé Partouche: Large Volume Supersymmetry Breaking without Decompactification Problem.- Lilia Anguelova: Glueball Inflation and Gauge/Gravity Duality.- Ovidiu Cristinel Stoica: Degenerate Metrics and Their Applications to Spacetime.- Denitsa Staicova and Plamen Fiziev: The Heun Functions and Their Applications in Astrophysics.- Chihiro Matsui: Boundary Effects on the Supersymmetric Sine-Gordon Model through Light-cone Lattice Regularization.- Roberto Bondesan and Thomas Quella: Infinite Dimensional Matrix Product States for Long-Range Quantum Spin Models.- Olena Vaneeva, Yuri Karadzhov, and Christodoulos Sophocleous: Group Analysis of a Class of Nonlinear Kolmogorov Equations.- Lachezar S. Georgiev: Thermoelectric Characteristics of Zk Parafermion Coulomb Islands.- Paolo Lorenzoni and Andrea Savoldi: First Order Hamiltonian Operators of Differential-Geometric Type in 2D.- Oksana Kuriksha and Olena Magda: Exact Solutions for Generalized KdV Equations with Variable Coefficients Using the Equivalence Method.- Pavle Pandzić: Classifying Aq(λ) Modules by Their Dirac Cohomology.- Nurit Barnea and Anna Melnikov: B-orbits in Abelian Nilradicals of Types B, C and D: Towards a Conjecture of Panyushev.- Vladimir K. Dobrev and Patrick Moylan: Anti de Sitter Holography via Sekiguchi Decomposition.- Patrick Moylan: Localization and the Canonical Commutation Relations.- Igor Salom and V. Dmitrasinović: Permutation-Symmetric Three-Body O(6) Hyperspherical Harmonics in Three Spatial Dimensions.- Todor Popov: Quantum Plactic and Pseudo-Plactic Algebras.- Stoimen Stoimenov and Malte Henkel: Conformal Invariance of the 1D Collisionless Boltzmann Equation.- Toshihisa Kubo: On Reducibility Criterions for Scalar Generalized Verma Modules Associated to Maximal Parabolic Subalgebras.- Elena Poletaeva: On FiniteW-Algebras for Lie Superalgebras in Non-Regular Case.- Sigiswald Barbier and Kevin Coulembier: The Joseph Ideal for sl(mjn).- Ludmil Hadjiivanov and Paolo Furlan: "Spread" Restricted Young Diagrams from a 2D WZNW Dynamical Quantum Group.- Tomoyuki Arakawa, Hiromichi Yamada, and Hiroshi Yamauchi: Vertex Operator Algebras Associated with Z/kZ-Codes.- Nikolay M. Nikolov: Vertex Algebras in Higher Dimensions Are Homotopy Equivalent to Vertex Algebras in Two Dimensions.- Anastasia Stavrova: Automorphisms of Multiloop Lie Algebras.- Maryna Nesterenko and Severin Posta: Contraction Admissible Pairs of Complex Six-Dimensional Nilpotent Lie Algebras.- R.M. Navarro: About Filiform Lie Algebras of Order 3.- Roy Oste and Joris Van der Jeugt: Algebraic Structures Related to Racah Doubles.- Antonio J. Calderón Martín and Diouf Mame: A Note on Strongly Graded Lie Algebras.- Tatyana Barron and David Itkin: Toeplitz Operators with Discontinuous Symbols on the Sphere.- J. Aragona, P. Catuogno, J.F. Colombeau, S.O. Juriaans, Ch. Olivera: Multiplication of Distributions in Mathematical Physics.- Alexander Ganchev: About Arbitrage and Holonomy.- Ilya I. Ryzhkov and Irina V. Stepanova: On Some Exact Solutions of Heat and Mass Transfer Equations with Variable Transport Coefficients.- Baran Serajelahi: A Star Product for the Volume Form Nambu-Poisson Structure on a Kähler Manifold

Blurb

This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.

Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.<

This is a large interdisciplinary and interrelated field, and the present volume is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.