2017, Contemporary mathematics, ISBN 9781470424602, Volume 683., x, 361 pages

Book

2013, Mathematical surveys and monographs, ISBN 9780821898468, Volume 189, xiii, 336

Book

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 12/2009, Volume 14, Issue 12, pp. 4071 - 4077

Lie algebras and Lie super algebra are constructed and integrable couplings of NLS–MKdV hierarchy are obtained. Furthermore, its Hamiltonian and...

Lie super algebra | Integrable coupling | Hamiltonian structure | Lie algebra | Super-trace identity | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | HAMILTONIAN-STRUCTURE | SPECTRAL PROBLEM | IDENTITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYSTEMS | Algebra | Couplings | Construction | Hierarchies | Computer simulation | Nonlinearity | Mathematical models

Lie super algebra | Integrable coupling | Hamiltonian structure | Lie algebra | Super-trace identity | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | HAMILTONIAN-STRUCTURE | SPECTRAL PROBLEM | IDENTITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYSTEMS | Algebra | Couplings | Construction | Hierarchies | Computer simulation | Nonlinearity | Mathematical models

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 12/2016, Volume 15, Issue 10

All solvable, indecomposable, finite-dimensional, complex Lie superalgebras g whose first derived ideal lies in its nilradical, and whose nilradical is a...

Solvable | Heisenberg Lie (super)algebras | nilpotent Lie (super)algebras | MATHEMATICS | MATHEMATICS, APPLIED | nilpotent Lie (super) algebras | ALGEBRAS | Heisenberg Lie (super) algebras

Solvable | Heisenberg Lie (super)algebras | nilpotent Lie (super)algebras | MATHEMATICS | MATHEMATICS, APPLIED | nilpotent Lie (super) algebras | ALGEBRAS | Heisenberg Lie (super) algebras

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 2010, Volume 15, Issue 8, pp. 2044 - 2049

Two different Lie super-algebras are constructed which establish two isospectral problems. Under the frame of the zero curvature equations, the corresponding...

Super-Hamiltonian structure | Super-Tu-hierarchy | Super-trace identity | Lie super-algebra | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | IDENTITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYSTEMS | SEMIDIRECT SUMS | COUPLINGS | Frames | Construction | Hierarchies | Computer simulation | Mathematical analysis | Nonlinearity | Mathematical models | Curvature

Super-Hamiltonian structure | Super-Tu-hierarchy | Super-trace identity | Lie super-algebra | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | IDENTITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYSTEMS | SEMIDIRECT SUMS | COUPLINGS | Frames | Construction | Hierarchies | Computer simulation | Mathematical analysis | Nonlinearity | Mathematical models | Curvature

Journal Article

中国物理快报：英文版, ISSN 0256-307X, 2010, Volume 27, Issue 4, pp. 5 - 8

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 2009, Volume 59, Issue 2, pp. 207 - 220

We prove the existence of a natural ∗ -Lie super-algebra bundle on any orientable WSD manifold of rank 3. We describe in detail the associated Lie...

Mirror symmetry | Lie super-algebras | Representations | MATHEMATICS, APPLIED | DUALITY | CALABI-YAU MANIFOLDS | PHYSICS, MATHEMATICAL | Algebra

Mirror symmetry | Lie super-algebras | Representations | MATHEMATICS, APPLIED | DUALITY | CALABI-YAU MANIFOLDS | PHYSICS, MATHEMATICAL | Algebra

Journal Article

International Journal of Algebra and Computation, ISSN 0218-1967, 11/2019, Volume 29, Issue 7, pp. 1235 - 1247

In this paper, we will first determine all the super-skewsymmetric super-biderivations of the twisted N = 2 superconformal algebra ℒ , and prove that every...

MATHEMATICS | super-skewsymmetric | super-biderivation | linear super-commuting map | Lie super-algebra

MATHEMATICS | super-skewsymmetric | super-biderivation | linear super-commuting map | Lie super-algebra

Journal Article

Journal of High Energy Physics, ISSN 1029-8479, 8/2019, Volume 2019, Issue 8, pp. 1 - 37

We show that the general method of Lie algebra expansions can be applied to re-construct several algebras and related actions for non-relativistic gravity that...

Space-Time Symmetries | Classical Theories of Gravity | Quantum Physics | Quantum Field Theories, String Theory | Chern-Simons Theories | Effective Field Theories | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | SUPERALGEBRAS | (SUPER)ALGEBRAS | PHYSICS, PARTICLES & FIELDS | Algebra | Gravity | Relativism | Gravitation | Supergravity | Lie groups | Relativistic effects | Physics - High Energy Physics - Theory

Space-Time Symmetries | Classical Theories of Gravity | Quantum Physics | Quantum Field Theories, String Theory | Chern-Simons Theories | Effective Field Theories | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | SUPERALGEBRAS | (SUPER)ALGEBRAS | PHYSICS, PARTICLES & FIELDS | Algebra | Gravity | Relativism | Gravitation | Supergravity | Lie groups | Relativistic effects | Physics - High Energy Physics - Theory

Journal Article

Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, 01/2010, Volume 17, Issue 2, pp. 159 - 166

Novikov super-algebras are related to quadratic conformal super-algebras which correspond to Hamiltonian pairs and play fundamental role in completely...

quadratic Novikov algebra | Novikov super-algebra | Lie-super algebra | Novikov algebra | quadratic Novikov super-algebra | MATHEMATICS | MATHEMATICS, APPLIED | HAMILTONIAN OPERATORS

quadratic Novikov algebra | Novikov super-algebra | Lie-super algebra | Novikov algebra | quadratic Novikov super-algebra | MATHEMATICS | MATHEMATICS, APPLIED | HAMILTONIAN OPERATORS

Journal Article

11.
Full Text
Heisenberg Lie superalgebras and their invariant superorthogonal and supersymplectic forms

Journal of Algebra, ISSN 0021-8693, 2011, Volume 332, Issue 1, pp. 71 - 86

Finite-dimensional complex Lie superalgebras of Heisenberg type obtained from a given Z 2 -homogeneous supersymplectic form defined on a vector superspace, are...

Nilpotent Lie (super)algebras | ad-Invariant supersymmetric bilinear forms | Solvable | Heisenberg Lie (super)algebras | Ad-Invariant supersymmetric bilinear forms | MATHEMATICS | ALGEBRAS

Nilpotent Lie (super)algebras | ad-Invariant supersymmetric bilinear forms | Solvable | Heisenberg Lie (super)algebras | Ad-Invariant supersymmetric bilinear forms | MATHEMATICS | ALGEBRAS

Journal Article

12.
Full Text
Computation of cohomology of Lie (super)algebra: algorithm, implementation and new results

Nuclear Inst. and Methods in Physics Research, A, ISSN 0168-9002, 2003, Volume 502, Issue 2, pp. 627 - 629

A new algorithmic approach to computation of cohomologies of Lie (super)algebras is described briefly. This approach, based on splitting the full cochain...

Computer algebra | Lie (super) algebra | Cohomology | INSTRUMENTS & INSTRUMENTATION | SPECTROSCOPY | cohomology | NUCLEAR SCIENCE & TECHNOLOGY | computer algebra | PHYSICS, PARTICLES & FIELDS

Computer algebra | Lie (super) algebra | Cohomology | INSTRUMENTS & INSTRUMENTATION | SPECTROSCOPY | cohomology | NUCLEAR SCIENCE & TECHNOLOGY | computer algebra | PHYSICS, PARTICLES & FIELDS

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 02/2017, Volume 43, pp. 151 - 157

•Based on a Lie super-algebra B(0,1), a new generalized super AKNS hierarchy is introduced.•By making use of the super-trace identity, the obtained generalized...

Super Hamiltonian structure | Self-consistent sources | A Lie super-algebra | TRANSFORMATION | MATHEMATICS, APPLIED | TRACE IDENTITY | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | PHYSICS, MATHEMATICAL | KDV HIERARCHY | SCHEME | POWERFUL TOOL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYSTEMS | Analysis | Algebra

Super Hamiltonian structure | Self-consistent sources | A Lie super-algebra | TRANSFORMATION | MATHEMATICS, APPLIED | TRACE IDENTITY | PHYSICS, FLUIDS & PLASMAS | EQUATIONS | PHYSICS, MATHEMATICAL | KDV HIERARCHY | SCHEME | POWERFUL TOOL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYSTEMS | Analysis | Algebra

Journal Article

14.
Full Text
Darboux transformation and analytic solutions for a generalized super-NLS-mKdV equation

Nonlinear Dynamics, ISSN 0924-090X, 10/2019, Volume 98, Issue 2, pp. 1491 - 1500

Darboux transformation is an efficient method for solving different nonlinear partial differential equations. In this paper, on the basis of a Lie...

Engineering | Vibration, Dynamical Systems, Control | Analytic solution | Classical Mechanics | Solitons | Automotive Engineering | Super-NLS-mKdV equation | Mechanical Engineering | Lie super-algebra | Darboux transformation | PERTURBATION | EXTENSION | RIEMANN-HILBERT APPROACH | ENGINEERING, MECHANICAL | ROSSBY SOLITARY WAVES | MECHANICS | BACKLUND-TRANSFORMATIONS | CUBIC NONLINEARITY | BOUSSINESQ | QUARTIC OPTICAL SOLITONS | CONSERVATION-LAWS | HIERARCHY | Algebra | Differential equations

Engineering | Vibration, Dynamical Systems, Control | Analytic solution | Classical Mechanics | Solitons | Automotive Engineering | Super-NLS-mKdV equation | Mechanical Engineering | Lie super-algebra | Darboux transformation | PERTURBATION | EXTENSION | RIEMANN-HILBERT APPROACH | ENGINEERING, MECHANICAL | ROSSBY SOLITARY WAVES | MECHANICS | BACKLUND-TRANSFORMATIONS | CUBIC NONLINEARITY | BOUSSINESQ | QUARTIC OPTICAL SOLITONS | CONSERVATION-LAWS | HIERARCHY | Algebra | Differential equations

Journal Article

Communications in Algebra, ISSN 0092-7872, 02/2018, Volume 46, Issue 2, pp. 684 - 704

We compare a number of different definitions of structure algebras and TKK constructions for Jordan (super)algebras appearing in the literature. We demonstrate...

TKK-construction | Lie superalgebras | Jordan superalgebras | MATHEMATICS | CLASSIFICATION | LIE SUPER-ALGEBRAS | Construction | Algebra | Mathematics - Rings and Algebras

TKK-construction | Lie superalgebras | Jordan superalgebras | MATHEMATICS | CLASSIFICATION | LIE SUPER-ALGEBRAS | Construction | Algebra | Mathematics - Rings and Algebras

Journal Article

São Paulo Journal of Mathematical Sciences, ISSN 1982-6907, 12/2019, Volume 13, Issue 2, pp. 615 - 627

In this paper, we first determine all the super-skewsymmetric super-biderivations of the super- $$\mathrm{BMS}_{3}$$ BMS 3 algebra. In particular, we find that...

17B68 | 17B40 | Linear super-commuting map | Super-skewsymmetric | Super-biderivation | Mathematics, general | Mathematics | 17B05 | Lie super-algebra

17B68 | 17B40 | Linear super-commuting map | Super-skewsymmetric | Super-biderivation | Mathematics, general | Mathematics | 17B05 | Lie super-algebra

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 08/2014, Volume 885, Issue 1, pp. 34 - 45

We show that the first-order D=4, N=1 pure supergravity lagrangian four-form can be obtained geometrically as a quadratic expression in the curvatures of the...

LIE-ALGEBRAS | INONU-WIGNER CONTRACTIONS | CONSTANT ELECTROMAGNETIC-FIELD | SUPERALGEBRA | EXPANSIONS | LOCAL REALIZATIONS | KINEMATICAL GROUPS | D=11 SUPERGRAVITY | (SUPER)ALGEBRAS | EXTENDED SUPERSPACES | PHYSICS, PARTICLES & FIELDS | Algebra | General Relativity and Quantum Cosmology | Mathematical Physics | Nuclear and High Energy Physics | High Energy Physics - Theory | Computer Science | Digital Libraries

LIE-ALGEBRAS | INONU-WIGNER CONTRACTIONS | CONSTANT ELECTROMAGNETIC-FIELD | SUPERALGEBRA | EXPANSIONS | LOCAL REALIZATIONS | KINEMATICAL GROUPS | D=11 SUPERGRAVITY | (SUPER)ALGEBRAS | EXTENDED SUPERSPACES | PHYSICS, PARTICLES & FIELDS | Algebra | General Relativity and Quantum Cosmology | Mathematical Physics | Nuclear and High Energy Physics | High Energy Physics - Theory | Computer Science | Digital Libraries

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 12/2018, Volume 108, Issue 12, pp. 2695 - 2727

The “brane scan” classifies consistent Green–Schwarz strings and membranes in terms of the invariant cocycles on super Minkowski spacetimes. The “brane...

Geometry | Rational homotopy theory | Cohomology of super Lie algebras | 81T30 (String and superstring theories | Theoretical, Mathematical and Computational Physics | Complex Systems | 55P62 (Rational homotopy theory) | other extended objects | Group Theory and Generalizations | M-theory | 17B56 (Cohomology of Lie (super)algebras) | Physics | SUPERGRAVITY | SUPERMEMBRANES | DIVISION-ALGEBRAS | PHYSICS, MATHEMATICAL | GEOMETRY | Algebra

Geometry | Rational homotopy theory | Cohomology of super Lie algebras | 81T30 (String and superstring theories | Theoretical, Mathematical and Computational Physics | Complex Systems | 55P62 (Rational homotopy theory) | other extended objects | Group Theory and Generalizations | M-theory | 17B56 (Cohomology of Lie (super)algebras) | Physics | SUPERGRAVITY | SUPERMEMBRANES | DIVISION-ALGEBRAS | PHYSICS, MATHEMATICAL | GEOMETRY | Algebra

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 4/2018, Volume 15, Issue 2, pp. 1 - 20

In this paper, we describe all subalgebras and automorphisms of simple noncommutative Jordan superalgebras $$K_3(\alpha ,\beta ,\gamma )$$ K3(α,β,γ) and...

Mathematics, general | Mathematics | 17C70 | 17C20 | MATHEMATICS | DELTA-SUPERDERIVATIONS | MATHEMATICS, APPLIED | LIE SUPER-ALGEBRAS | MAXIMAL SUBALGEBRAS | CLASSIFICATION | FINITE-DIMENSIONAL JORDAN | DERIVATIONS | Mathematics - Rings and Algebras

Mathematics, general | Mathematics | 17C70 | 17C20 | MATHEMATICS | DELTA-SUPERDERIVATIONS | MATHEMATICS, APPLIED | LIE SUPER-ALGEBRAS | MAXIMAL SUBALGEBRAS | CLASSIFICATION | FINITE-DIMENSIONAL JORDAN | DERIVATIONS | Mathematics - Rings and Algebras

Journal Article

Journal of Algebra, ISSN 0021-8693, 12/2014, Volume 419, pp. 167 - 222

This paper is a resolution of three related problems proposed by Yu.I. Manin and V. Kac for the so-called exceptional Lie superalgebras F(4) and G(3). The...

Lie superalgebras | Blocks | Exceptional Lie superalgebras | Characters | Representation theory | Exceptional Lie algebras | Cohomology groups | Borel–Weil–Bott theorem | Borel-Weil-Bott theorem | SUPERGROUPS | SUPER-ALGEBRAS | CHARACTER FORMULAS | MATHEMATICS | COHOMOLOGY

Lie superalgebras | Blocks | Exceptional Lie superalgebras | Characters | Representation theory | Exceptional Lie algebras | Cohomology groups | Borel–Weil–Bott theorem | Borel-Weil-Bott theorem | SUPERGROUPS | SUPER-ALGEBRAS | CHARACTER FORMULAS | MATHEMATICS | COHOMOLOGY

Journal Article

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