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.

Presents a unique balanced representation of mathematicians, mathematical physicists, and theoretical physicists Serves as interface of the scientific interests and methods of these groups of scientists Covers the entire field of Lie Theory in its widest sense with its applications in many diverse facets of physics

Inhalt
Plenary Talks: T. Kobayashi, Multiplicity in Restricting Minimal Representations.- Yang-Hui He, From the String Landscape to the Mathematical Landscape: a Machine-Learning Outlook.- I. Todorov, Octonionic Clifford Algebra for the Internal Space of the Standard Model.- P. Vitale, The Jacobi Sigma Model.- P. Aschieri, Levi-Civita Connections on Braided Algebras.- N. Bobev, Notes on AdS4 Holography and Higher-Derivative Supergravity.- T. Brzezinski, Homothetic Rota-Baxter Systems and Dyckm-Algebras.- M. Henkel, Quantum Dynamics Far from Equilibrium: a Case Study in the Spherical Model.- Hankyung Ko and V. Mazorchuk, On First Extensions in S -Subcategories of O.- Robert de Mello Koch and Sanjaye Ramgoolam, Higher Dimensional CFTs as 2D Conformally-Equivariant Topological Field Theories.- G. Manolakos, G. Patellis and G. Zoupanos, Reducing the N = 1, 10D E8 Gauge Theory over a Modified Flag Manifold.- String Theories, (Super-)Gravity, Cosmology: Andre Alves Lima, Galen M. Sotkov and Marian Stanishkov, Ramond States of the D1-D5 CFT Away from the Free Orbifold Point.- L. Anguelova, Primordial Black Hole Generation in a Two-field Inflationary Model.- D. Staicova, Late Time Cosmic Acceleration with Uncorrelated Baryon Acoustic Oscillations.- L. Ravera, On the Hidden Symmetries of D = 11 Supergravity.- F. Nieri, Defects at the Intersection: the Supergroup Side.- T. Masuda, A New S-matrix Formula and Extension of the State Space in Open String Field Theory.- E. Boffo, Dual Dilaton with R and Q Fluxes.- Representation Theory: E. Poletaeva, On 1-Dimensional Modules over the Super-Yangian of the Superalgebra Q(1).- N. I. Stoilova and Joris Van der Jeugt, A Klein Operator for Paraparticles.- G. Sengor and C. Skordis, Principal and Complementary Series Representations at the Late-Time Boundary of de Sitter.- S. Aoki, Janos Balog, T. Onogi, and S. Yokoyama, Bulk Reconstruction from a Scalar CFT at the Boundary by the Smearing with the Flow Equation.- Y. Wang and Chih-Hao Fu, Building Momentum Kernel from Shapovalov Form.- Ilia Smilga, Action of w0 on VL for Orthogonal and Exceptional Groups.- Ood Shabtai, Pairs of Spectral Projections of Spin Operators.- Integrable Systems: Jean-Emile Bourgine, Algebraic Engineering and Integrable Hierarchies.- Cestm ´r Burd´k and O. Navratil, Nested Bethe Ansatz for RTTAlgebra An.- O. Vaneeva, O. Magda and A. Zhalij, Lie Reductions and Exact Solutions of Generalized Kawahara Equations.- Y. Nasuda, Several Exactly Solvable Quantum Mechanical Systems and the SWKB Quantization Condition.- A. Pribytok, Automorphic Symmetries and AdSn Integrable Deformations.- Applications to Quantum Theory: M. Kirchbach, T. Popov, and J.-A. Vallejo, The Conformal-SymmetryColor-Neutrality Connection in Strong Interaction.- I. Salom and N. Manojlovic, s(2) Gaudin Model with General Boundary Terms.- T. Barron and A. Kazachek, Entanglement of Mixed States in Kahler Quantization.- J. Alnefjord, A. Lifson, C. Reuschle, and M. Sjodahl,The Chirality-Flow Formalism for Standard Model Calculations.- F. Kuipers, Spacetime Stochasticity and Second Order Geometry.- Special Mathematical Results: P. Moylan, Velocity Reciprocity in Flat and Curved Space-Time.- S. Stoimenov and M. Henkel, Meta-Schrodinger Transformations.- Hulya Arg ¨ uz¨, The Quantum Mirror to the Quartic del Pezzo Surface.- A. Ganchev, Bidirectional Processes - in Category Theory, Physics, Engineering.- Gauge Theories and Applications: Richard S. Garavuso, Nonholomorphic Superpotentials in Heterotic Landau-Ginzburg Models.- F. Feruglio, Automorphic Forms and Fermion Masses.- T. Ishibashi, Wilson Lines and Their Laurent Positivity.- Maro Cvitan, Predrag Dominis Prester, Stefano Gregorio Giaccari, Mateo Paulisi c´, and Ivan Vukovic´, Gauging Higher-Spin-Like Symmetries Using the Moyal Product.- N. Ikeda and S. Sasaki, Integration of Double Field Theory Algebroids and Pre-rackoid in Doubled Geometry.- H. Mori, S. Sasaki, K. Shiozawa, Doubled Aspects of Algebroids and Gauge Symmetry in Double Field Theory.- C. Anghel and D. Cheptea, Lie Algebroids and Weight Systems.- Structures on Lie Groups and Lie Algebras: K. Arashi, Visible Actions of Certain Affine Transformation Groups of a Siegel Domain of the Second Kind.- A. Brus, Jir´ Hrivnak´ and L. Motlochova´, Quantum Particle on Lattices in Weyl Alcoves.- A. Latorre and L. Ugarte, Abelian J-Invariant Ideals on Nilpotent Lie Algebras.- Alexis Langlois-Remillard, The Dihedral DunklDirac Symmetry Algebra with Negative Clifford Signature.- Tekin Karadag, Lie Structure on Hopf Algebra Cohomology.- Esther Garca, Miguel Gomez Lozano, and Ruben Munoz Alcazar, Filtration Associated to an Abelian Inner Ideal and the Speciality of the Subquotient of a Lie Algebra.- Esther Garc´a, Miguel Gomez Lozano, and Guillermo Vera de Salas, Nilpotent Inner Derivations in Prime Superalgebras.