Dictionary on Lie Superalgebras

Abstract

The main definitions and properties of Lie superalgebras are proposed a la facon de a short dictionary, the different items following the alphabetical order. The main topics deal with the structure of simple Lie superalgebras and their finite dimensional representations; rather naturally, a few pages are devoted to supersymmetry. This modest booklet has two ambitious goals: to be elementary and easy to use. The beginner is supposed to find out here the main concepts on superalgebras, while a more experimented theorist should recognize the necessary tools and informations for a specific use.

145p LaTeX Document, also available at http://lapphp0.in2p3.fr/preplapp/psth/DICTIONARY_SUPER.ps.gz

References in corpus (1)

• Strings from $N=2$ Gauged Wess-Zumino-Witten Models

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• Foundations of the AdS_5 x S^5 Superstring. Part I
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• Strings on Semisymmetric Superspaces
• Integrability, spin-chains and the AdS3/CFT2 correspondence
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• Ghost D-branes
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• Review of AdS/CFT Integrability, Chapter VI.1: Superconformal Symmetry
• Dilatation operator in (super-)Yang-Mills theories on the light-cone
• Supersymmetry and homogeneity of M-theory backgrounds
• Hidden symmetries of integrable conformal mechanical systems
• ABC of N=8, d=1 supermultiplets
• The Energy-Momentum Tensor(s) in Classical Gauge Theories
• Superconformal Multi-Black Hole Moduli Spaces in Four Dimensions
• Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
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• New D(2,1;alpha) Mechanics with Spin Variables
• N=8 superconformal mechanics
• The Quantum Superstring as a WZNW Model with N=2 Superconformal Symmetry
• Many-particle mechanics with D(2,1;alpha) superconformal symmetry
• Self-Duality of Green-Schwarz Sigma-Models
• Yangians, S-matrices and AdS/CFT
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• N=4 supersymmetric 3-particles Calogero model
• The Exact S-Matrix for an osp(2|2) Disordered System
• Three point functions in higher spin AdS_3 supergravity
• Global Supersymmetry on Curved Spaces in Various Dimensions
• Superstrings in AdS
• q-Deformed Supersymmetry and Dynamic Magnon Representations
• Potentials in N=4 superconformal mechanics
• New Model of N=8 Superconformal Mechanics
• Nearing the Horizon of a Heterotic String
• N=4 superconformal n-particle mechanics via superspace
• Gauge Theory on Noncommutative Supersphere from Supermatrix Model
• Integrable quantum field theories with supergroup symmetries: the $OSP(1/2)$ case
• Conical defects and N=2 higher spin holography
• Biharmonic Superspace for N=4 Mechanics
• Rigid 4D N=2 supersymmetric backgrounds and actions
• Supergroup Structure of Jackiw-Teitelboim Supergravity
• Superconformal mechanics in SU(2|1) superspace
• Universal R-matrix as integral operator
• From $s{l}_q(2)$ to a Parabosonic Hopf Algebra
• Critical scaling dimension of D-module representations of N=4,7,8 Superconformal Algebras and constraints on Superconformal Mechanics
• Geometry of branes on supergroups
• Boundary Correlators in Supergroup WZNW Models
• Superconformal operators in Yang-Mills theories on the light-cone
• Wigner Oscillators, Twisted Hopf Algebras and Second Quantization
• The algebraic structure of Galilean superconformal symmetries
• Exceptional N=6 and N=2 AdS_4 Supergravity, and Zero-Center Modules
• Superspin chains and supersymmetric gauge theories
• Dualities from higher-spin supergravity
• Comments on Determinant Formulas for General CFTs
• New Compact Construction of Eigenstates for Supersymmetric Spin Chains
• Superconformal blocks from Wilson lines with loop corrections
• From worldline to quantum superconformal mechanics with/without oscillatorial terms: $D(2,1;\alpha )$ and $sl(2|1)$ models
• SU(2|2) supersymmetric mechanics
• Super-de Sitter and alternative super-Poincaré symmetries
• Supergravity in Two Spacetime Dimensions
• The plane-wave spectrum from the worldsheet
• Supergroup - extended super Liouville correspondence
• Three dimensional N=4 supersymmetric mechanics with Wu-Yang monopole
• N=2 supersymmetric extension of the Tremblay-Turbiner-Winternitz Hamiltonians on a plane
• N=4 Supersymmetry and the BPST Instanton
• Particle in a self-dual dyon background: hidden free nature, and exotic superconformal symmetry
• Integrable strings for AdS/CFT
• The Structure of BPS Equations for Ambi-polar Microstate Geometries
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• New realizations of the supergroup D(2,1;α) in N=4 superconformal mechanics
• $\mathcal{N}=2$ Super-Teichmüller Theory
• $sl(2|1{)}^{(2)}$ Gaudin Magnet and its associated Knizhnik-Zamolodchikov equation
• Multiparticle $\mathcal{N}=8$ mechanics with $F(4)$ superconformal symmetry
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• Yangian of the Strange Lie Superalgebra of ${\mathbf{Q}}_{\mathbf{n}-1}$ Type, Drinfel'd Approach
• Dynamic Lattice Supersymmetry in gl(n|m) Spin Chains
• Conformal and non-conformal hyperloop deformations of the 1/2 BPS circle
• N=4 l-conformal Galilei superalgebra
• Analytic Bethe Ansatz and Baxter equations for long-range psl(2|2) spin chain
• Superconformal Quantum Mechanics from M2-branes
• Branes in JT (super)gravity from group theory
• Determinant Formula for Parabolic Verma Modules of Lie Superalgebras
• Primary fields and screening currents of gl(2|2) non-unitary conformal field theory
• Lax Operator and superspin chains from 4D CS gauge theory
• N=4 Superconformal Mechanics and Black Holes
• The Yangian of sl(n|m) and the universal R-matrix
• Simple prolongs of the non-positive parts of graded Lie algebras with Cartan matrix in characteristic 2
• Lax pairs for new ${\mathbb{Z}}_N$-symmetric coset $\sigma$-models and their Yang-Baxter deformations
• Gaudin models with ${\CU}_q(\mathfrak{osp}(1 | 2))$ symmetry
• Minimal $\mathcal{N}=4$ topologically massive supergravity
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• Finite $W$-superalgebras and quadratic spacetime supersymmetries
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