Dobrev V. (ed.) Lie Theory and Its Applications in Physics: Sofia, Bulgaria, June 2021

Singapore: Springer, 2023. — 526 p.This volume presents modern trends in the area of symmetries and their applications based on contributions to the Workshop "Lie Theory and Its Applications in Physics" held in Sofia, Bulgaria (on-line) in June 2021.
Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is 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 meant in their widest sense, i.e., 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, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a big interdisciplinary and interrelated field.
The topics covered in this Volume are the most modern trends in the field of the Workshop: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, Exceptional quantum algebra for the standard model of particle physics, Gauge Theories and Applications, Structures on Lie Groups and Lie Algebras.
This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.Preface
List of Registered LT-14 Participants
*-1pc Plenary Talks
Multiplicity in Restricting Minimal Representations
From the String Landscape to the Mathematical Landscape: A Machine-Learning Outlook
Octonionic Clifford Algebra for the Internal Space of the Standard Model
The Jacobi Sigma Model
Levi-Civita Connections on Braided Algebras
Notes on AdS4 Holography and Higher-Derivative Supergravity
Homothetic Rota–Baxter Systems and Dyckm-Algebras
Quantum Dynamics Far from Equilibrium: A Case Study in the Spherical Model
On First Extensions in mathcalS-Subcategories of mathcalO
Higher Dimensional CFTs as 2D Conformally-Equivariant Topological Field Theories
Reducing the N = 1, 10-d, E8 Gauge Theory over a Modified Flag Manifold
*-1pc String Theories, (Super-)Gravity, Cosmology
Ramond States of the D1-D5 CFT Away from the Free Orbifold Point
Primordial Black Hole Generation in a Two-Field Inflationary Model
Late Time Cosmic Acceleration with Uncorrelated Baryon Acoustic Oscillations
On the Hidden Symmetries of D=11 Supergravity
Defects at the Intersection: The Supergroup Side
A New S-matrix Formula and Extension of the State Space in Open String Field Theory
Dual Dilaton with mathcalR and mathcalQ Fluxes
*-1pc Representation Theory
On 1-Dimensional Modules over the Super-Yangian of the Superalgebra Q(1)
A Klein Operator for Paraparticles
Bulk Reconstruction from a Scalar CFT at the Boundary by the Smearing with the Flow Equation
Building Momentum Kernel from Shapovalov Form
Action of w0 on VL for Orthogonal and Exceptional Groups
Pairs of Spectral Projections of Spin Operators
*-1pc Integrable Systems
Algebraic Engineering and Integrable Hierarchies
Nested Bethe Ansatz for RTT–Algebra mathcalAn
Lie Reductions and Exact Solutions of Generalized Kawahara Equations
Several Exactly Solvable Quantum Mechanical Systems and the SWKB Quantization Condition
Automorphic Symmetries and AdSn Integrable Deformations
*-1pc Applications to Quantum Theory
The Conformal-Symmetry–Color-Neutrality Connection in Strong Interaction
sell(2) Gaudin Model with General Boundary Terms
Entanglement of Mixed States in Kähler Quantization
The Chirality-Flow Formalism for Standard Model Calculations
Spacetime Stochasticity and Second Order Geometry
*-1pc Special Mathematical Results
Velocity Reciprocity in Flat and Curved Space-Time
Meta-Schrödinger Transformations
The Quantum Mirror to the Quartic del Pezzo Surface
Bidirectional Processes—In Category Theory, Physics, Engineering, …
*-1pc Gauge Theories and Applications
Nonholomorphic Superpotentials in Heterotic Landau-Ginzburg Models
Automorphic Forms and Fermion Masses
Wilson Lines and Their Laurent Positivity
Gauging Higher-Spin-Like Symmetries Using the Moyal Product
Integration of Double Field Theory Algebroids and Pre-rackoid in Doubled Geometry
Doubled Aspects of Algebroids and Gauge Symmetry in Double Field Theory
Lie Algebroids and Weight Systems
*-1pc Structures on Lie Groups and Lie Algebras
Visible Actions of Certain Affine Transformation Groups of a Siegel Domain of the Second Kind
Quantum Particle on Lattices in Weyl Alcoves
Abelian J-Invariant Ideals on Nilpotent Lie Algebras
The Dihedral Dunkl–Dirac Symmetry Algebra with Negative Clifford Signature
Lie Structure on Hopf Algebra Cohomology
Filtration Associated to an Abelian Inner Ideal and the Speciality of the Subquotient of a Lie Algebra
Nilpotent Inner Derivations in Prime Superalgebras