International Journal of Modern Physics A, ISSN 0217-751X, 07/2018, Volume 33, Issue 20, p. 1850117

We propose a generalization of Schramm–Loewner evolution (SLE) that has internal degrees of freedom described by an affine Lie superalgebra. We give a general...

conformal field theory | Lie superalgebra | Schramm-Loewner evolution | MARTINGALES | STOCHASTIC EVOLUTIONS | SCALING LIMITS | REPRESENTATIONS | GROWTH-PROCESSES | ALGEBRA | PHYSICS, NUCLEAR | SLE | CONFORMAL FIELD-THEORIES | CRITICAL PERCOLATION | 2 DIMENSIONS | PHYSICS, PARTICLES & FIELDS

conformal field theory | Lie superalgebra | Schramm-Loewner evolution | MARTINGALES | STOCHASTIC EVOLUTIONS | SCALING LIMITS | REPRESENTATIONS | GROWTH-PROCESSES | ALGEBRA | PHYSICS, NUCLEAR | SLE | CONFORMAL FIELD-THEORIES | CRITICAL PERCOLATION | 2 DIMENSIONS | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, 6/2016, Volume 7, Issue 2, pp. 141 - 155

We investigate the first cohomology space associated with the embedding of the Lie Orthosymplectic superalgebra $${\mathfrak {osp}}(3|2)$$ osp ( 3 | 2 ) on the...

Superpseudodifferential operators | 53D55 | 14F43 | Mathematics | Cohomology | Orthosymplectic superalgebra | Poisson superalgebra | 17B56 | Operator Theory | Algebra | Functional Analysis | 14F40 | Analysis | Applications of Mathematics | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | CONTACT VECTOR-FIELDS | ALGEBRA | Lie superalgebras | Research | Cohomology theory | Mathematical research

Superpseudodifferential operators | 53D55 | 14F43 | Mathematics | Cohomology | Orthosymplectic superalgebra | Poisson superalgebra | 17B56 | Operator Theory | Algebra | Functional Analysis | 14F40 | Analysis | Applications of Mathematics | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | CONTACT VECTOR-FIELDS | ALGEBRA | Lie superalgebras | Research | Cohomology theory | Mathematical research

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 2019, Volume 52, Issue 13

The algebraic structure generated by the creation and annihilation operators of a system of m parafermions and n parabosons, satisfying the mutual parafermion...

parastatistics | Fock space | Lie superalgebra | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | PARA-BOSE

parastatistics | Fock space | Lie superalgebra | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | PARA-BOSE

Journal Article

Journal of Algebra, ISSN 0021-8693, 05/2019, Volume 525, pp. 191 - 233

In this paper, a notion of affine walled Brauer–Clifford superalgebras BCr,taff is introduced over an arbitrary integral domain R containing 2−1. These...

Queer Lie superalgebra | Affine walled Brauer–Clifford superalgebras | Schur–Weyl duality | MATHEMATICS | ALGEBRAS | REPRESENTATIONS | Schur-Weyl duality | Affine walled Brauer-Clifford superalgebras | Algebra

Queer Lie superalgebra | Affine walled Brauer–Clifford superalgebras | Schur–Weyl duality | MATHEMATICS | ALGEBRAS | REPRESENTATIONS | Schur-Weyl duality | Affine walled Brauer-Clifford superalgebras | Algebra

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 11/2019, Volume 42, Issue 6, pp. 3289 - 3301

We describe degenerations of three-dimensional Jordan superalgebras over $$\mathbb {C}$$ C . In particular, we describe all irreducible components in the...

17C10 | Orbit closure | Jordan superalgebra | Rigid superalgebra | Mathematics, general | Mathematics | Degeneration | 17C70 | Applications of Mathematics | MATHEMATICS | NILPOTENT LIE-ALGEBRAS | CLASSIFICATION | GRADED CONTRACTIONS | Mathematics - Rings and Algebras

17C10 | Orbit closure | Jordan superalgebra | Rigid superalgebra | Mathematics, general | Mathematics | Degeneration | 17C70 | Applications of Mathematics | MATHEMATICS | NILPOTENT LIE-ALGEBRAS | CLASSIFICATION | GRADED CONTRACTIONS | Mathematics - Rings and Algebras

Journal Article

Fortschritte der Physik, ISSN 0015-8208, 09/2017, Volume 65, Issue 9, pp. 1700005 - n/a

In this work, we expand the hidden AdS‐Lorentz superalgebra underlying D=4 supergravity, reaching a (hidden) Maxwell superalgebra. The latter can be viewed as...

ALGEBRAS | PARTICLES | PHYSICS, MULTIDISCIPLINARY | GRAVITY | EXPANSION | Analysis | Algebra | Physics - High Energy Physics - Theory

ALGEBRAS | PARTICLES | PHYSICS, MULTIDISCIPLINARY | GRAVITY | EXPANSION | Analysis | Algebra | Physics - High Energy Physics - Theory

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 12/2012, Volume 11, Issue 6, pp. 1250119 - 1250129

In this paper, we recall the Balinsky-Novikov (BN) superalgebras and revisit the approach of constructing an infinite-dimensional Lie superalgebra by a kind of...

Balinsky-Novikov superalgebra | Beltrami superalgebra | GSW superalgebra | Lie superalgebra | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | CALCULUS | CLASSIFICATION | NEVEU-SCHWARZ | VIRASORO | Boron nitride | Belts | Construction | Recall | Algebra

Balinsky-Novikov superalgebra | Beltrami superalgebra | GSW superalgebra | Lie superalgebra | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | CALCULUS | CLASSIFICATION | NEVEU-SCHWARZ | VIRASORO | Boron nitride | Belts | Construction | Recall | Algebra

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 1998, Volume 252, Issue 3, pp. 565 - 585

The Lie superalgebra sl( r+1∣ s+1) admits several inequivalent choices of simple root systems. We have carried out analytic Bethe ansatz for any simple root...

Solvable lattice model | Transfer matrix | Analytic Bethe ansatz | Young superdiagram | Lie superalgebra | T-system | solvable lattice model | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | analytic Bethe ansatz | young superdiagram | T-J MODEL | IDENTITY | transfer matrix | ALGEBRAS | DIMENSION | TRANSFER-MATRICES | SOLVABLE LATTICE MODELS | VERTEX MODELS | FORMULAS | JACOBI-TRUDI

Solvable lattice model | Transfer matrix | Analytic Bethe ansatz | Young superdiagram | Lie superalgebra | T-system | solvable lattice model | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | analytic Bethe ansatz | young superdiagram | T-J MODEL | IDENTITY | transfer matrix | ALGEBRAS | DIMENSION | TRANSFER-MATRICES | SOLVABLE LATTICE MODELS | VERTEX MODELS | FORMULAS | JACOBI-TRUDI

Journal Article

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, ISSN 0034-5318, 2019, Volume 55, Issue 1, pp. 123 - 188

Let g = g((0) over bar) + g((1) over bar) be a basic Lie superalgebra over C, and e a minimal nilpotent element in g((0) over bar). Set W-x' to be the refined...

modular representations of Lie (super)algebras | MATHEMATICS | basic (classical) Lie superalgebras | ALGEBRAS | SLICES | FINITE | Finite W-(super)algebras | (super) Kac-Weisfeiler conjecture (property) for modular Lie (super)algebras | IDEALS | minimal nilpotent elements | QUANTUM REDUCTION

modular representations of Lie (super)algebras | MATHEMATICS | basic (classical) Lie superalgebras | ALGEBRAS | SLICES | FINITE | Finite W-(super)algebras | (super) Kac-Weisfeiler conjecture (property) for modular Lie (super)algebras | IDEALS | minimal nilpotent elements | QUANTUM REDUCTION

Journal Article

Journal of Algebra, ISSN 0021-8693, 2010, Volume 324, Issue 7, pp. 1513 - 1528

The purpose of this paper is to study Hom-Lie superalgebras, that is a superspace with a bracket for which the superJacobi identity is twisted by a...

Hom-Lie superalgebra | Hom-associative superalgebra | Hom-Lie admissible superalgebra | Lie admissible superalgebra | q-Witt superalgebra | Q-Witt superalgebra

Hom-Lie superalgebra | Hom-associative superalgebra | Hom-Lie admissible superalgebra | Lie admissible superalgebra | q-Witt superalgebra | Q-Witt superalgebra

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 12/2017, Volume 27, Issue 4, pp. 3063 - 3082

The purpose of this paper is to study the relationships between a Hom-Lie superalgebra and its induced 3-ary-Hom-Lie superalgebra. We provide an overview of...

Central extension | 3-ary Hom-Lie superalgebras | Theoretical, Mathematical and Computational Physics | Hom-Lie superalgebras | Cohomology | Solvable | Physics | 17B55 | Mathematical Methods in Physics | 17B30 | 17B70 | Applications of Mathematics | Physics, general | 17A40 | MATHEMATICS, APPLIED | EXTENSIONS | PHYSICS, MATHEMATICAL | Mathematics - Rings and Algebras

Central extension | 3-ary Hom-Lie superalgebras | Theoretical, Mathematical and Computational Physics | Hom-Lie superalgebras | Cohomology | Solvable | Physics | 17B55 | Mathematical Methods in Physics | 17B30 | 17B70 | Applications of Mathematics | Physics, general | 17A40 | MATHEMATICS, APPLIED | EXTENSIONS | PHYSICS, MATHEMATICAL | Mathematics - Rings and Algebras

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 10/2016, Volume 284, Issue 1-2, pp. 595 - 613

We give a proof of a Schur-Weyl duality statement between the Brauer algebra and the ortho-symplectic Lie superalgebra .

Mixed tensor space | Invariant theory | Double centralizer | Brauer algebra | Lie superalgebra | MATHEMATICS | SUPERGROUPS | REPRESENTATIONS | CENTRALIZER ALGEBRAS | Algebra

Mixed tensor space | Invariant theory | Double centralizer | Brauer algebra | Lie superalgebra | MATHEMATICS | SUPERGROUPS | REPRESENTATIONS | CENTRALIZER ALGEBRAS | Algebra

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 08/2015, Volume 48, Issue 31, pp. 1 - 20

We describe the algebra of invariants of the vacuum module associated with an affinization of the Lie superalgebra gl(1 vertical bar 1). We give a formula for...

plane partitions | vacuum module | Lie superalgebra | POLYNOMIALS | SHIFT | ALGEBRAS | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | CRITICAL-LEVEL | GAUDIN MODEL | PHYSICS, MATHEMATICAL | Functions (mathematics) | Theorems | Algebra | Mathematical analysis | Modules | Polynomials | Invariants | Symmetry

plane partitions | vacuum module | Lie superalgebra | POLYNOMIALS | SHIFT | ALGEBRAS | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | CRITICAL-LEVEL | GAUDIN MODEL | PHYSICS, MATHEMATICAL | Functions (mathematics) | Theorems | Algebra | Mathematical analysis | Modules | Polynomials | Invariants | Symmetry

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2019, Volume 147, Issue 8, pp. 3191 - 3207

We define global and local Weyl modules for Lie superalgebras of the form \mathfrak{g} \otimes A, where A is an associative commutative unital...

MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | Kac module | Weyl module | basic Lie superalgebra | Lie superalgebra | tensor product

MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | Kac module | Weyl module | basic Lie superalgebra | Lie superalgebra | tensor product

Journal Article

Journal of Algebra, ISSN 0021-8693, 01/2015, Volume 422, pp. 1 - 10

We study asymptotic behaviour of graded codimensions of Lie superalgebra b(2). We prove that graded PI-exponent exists and is equal to 3+23.

Graded polynomial identities | PI-exponent | Lie superalgebras | Codimensions | Exponential growth | MATHEMATICS | ALGEBRAS | GROWTH | Algebra | Mathematics - Rings and Algebras

Graded polynomial identities | PI-exponent | Lie superalgebras | Codimensions | Exponential growth | MATHEMATICS | ALGEBRAS | GROWTH | Algebra | Mathematics - Rings and Algebras

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 10/2014, Volume 84, pp. 1 - 7

This paper considers eight series of infinite-dimensional simple Lie superalgebras of vector fields over a field of characteristic zero. It is proved that...

Grading | Hom–Lie superalgebra structure | Lie superalgebra | Hom-Lie superalgebra structure

Grading | Hom–Lie superalgebra structure | Lie superalgebra | Hom-Lie superalgebra structure

Journal Article

Journal of Algebra, ISSN 0021-8693, 05/2016, Volume 454, pp. 433 - 474

We introduce a new family of superalgebras, the quantum walled Brauer–Clifford superalgebras BCr,s(q). The superalgebra BCr,s(q) is a quantum deformation of...

Queer Lie superalgebra | Bead tangle algebra | Quantum walled Brauer–Clifford superalgebra | Centralizer algebra | q-Schur superalgebra | Quantum walled Brauer-Clifford superalgebra | Secondary | Q-Schur superalgebra | Primary | MIXED TENSOR REPRESENTATIONS | LIE-SUPERALGEBRAS | LINEAR-GROUPS | CHARACTERS | SPACE | MATHEMATICS | CENTRALIZER ALGEBRAS | DUALITY | Algebra

Queer Lie superalgebra | Bead tangle algebra | Quantum walled Brauer–Clifford superalgebra | Centralizer algebra | q-Schur superalgebra | Quantum walled Brauer-Clifford superalgebra | Secondary | Q-Schur superalgebra | Primary | MIXED TENSOR REPRESENTATIONS | LIE-SUPERALGEBRAS | LINEAR-GROUPS | CHARACTERS | SPACE | MATHEMATICS | CENTRALIZER ALGEBRAS | DUALITY | Algebra

Journal Article

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Full Text
Eleven-dimensional supergravity from filtered subdeformations of the Poincaré superalgebra

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 06/2016, Volume 49, Issue 29, p. 295204

We summarise recent results concerning the classification of filtered deformations of graded subalgebras of the Poincare superalgebra in eleven dimensions,...

supergravity | Spencer cohomology | Lie superalgebras | filtered deformations | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

supergravity | Spencer cohomology | Lie superalgebras | filtered deformations | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 04/2015, Volume 48, Issue 15

An orthogonal basis of weight vectors for a class of infinite-dimensional representations of the orthosymplectic Lie superalgebra osp(2m+ 1 vertical bar 2n) is...

parastatistics | osp(2m + 1?2n) | Lie superalgebra | PARTICLES | PHYSICS, MULTIDISCIPLINARY | osp(2m+1 vertical bar 2n) | QUANTIZATION | PHYSICS, MATHEMATICAL | PARA-BOSE

parastatistics | osp(2m + 1?2n) | Lie superalgebra | PARTICLES | PHYSICS, MULTIDISCIPLINARY | osp(2m+1 vertical bar 2n) | QUANTIZATION | PHYSICS, MATHEMATICAL | PARA-BOSE

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 09/2013, Volume 30, Issue 17, pp. 175016 - 20

We show how the rigid conformal supersymmetries associated with a certain class of pseudo-Riemannian spin manifolds define a Lie superalgebra. The even part of...

QUANTUM SCIENCE & TECHNOLOGY | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | CONSTRUCTION | GRADED LIE-ALGEBRAS | CLASSIFICATION | SPINORS | PHYSICS, PARTICLES & FIELDS | Manifolds | Supersymmetry | Flats | Constants | Representations | Quantum gravity | Symmetry | Physics - High Energy Physics - Theory

QUANTUM SCIENCE & TECHNOLOGY | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | CONSTRUCTION | GRADED LIE-ALGEBRAS | CLASSIFICATION | SPINORS | PHYSICS, PARTICLES & FIELDS | Manifolds | Supersymmetry | Flats | Constants | Representations | Quantum gravity | Symmetry | Physics - High Energy Physics - Theory

Journal Article

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