JOURNAL OF ALGEBRA AND ITS APPLICATIONS, ISSN 0219-4988, 11/2019, Volume 18, Issue 11

In this paper, we define and study Whittaker modules for the super-Viraoro algebras, including the Neveu-Schwarz algebra and the Ramond algebra. We classify...

MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATION-THEORY | Whittaker modules | super-Virasoro algebras | LIE-ALGEBRA | CATEGORIES | VECTORS | NEVEU-SCHWARZ

MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATION-THEORY | Whittaker modules | super-Virasoro algebras | LIE-ALGEBRA | CATEGORIES | VECTORS | NEVEU-SCHWARZ

Journal Article

Axioms, ISSN 2075-1680, 07/2019, Volume 8, Issue 3, p. 82

We explicitly calculate the branching functions arising from the tensor product decompositions between level 2 and principal admissible representations over sl...

super-Virasoro algebras | characters | branching functions | affine Lie algebras | admissible representations

super-Virasoro algebras | characters | branching functions | affine Lie algebras | admissible representations

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 06/2015, Volume 26, Issue 7, pp. 1550041 - 1-1550041-15

The structure theory of a class of generalized loop super-Virasoro algebras is studied in this paper. In particular, the derivation algebras, the automorphism...

derivations | 2-cocycles | Generalized loop super-Virasoro algebras | automorphisms | second cohomology groups | REPRESENTATIONS | HARISH-CHANDRA MODULES | WITT TYPE | INTERMEDIATE SERIES | LIE-ALGEBRAS | MATHEMATICS | WZW MODEL | 2ND COHOMOLOGY | Algebra | Derivation | Mathematical analysis | Automorphisms | Group theory

derivations | 2-cocycles | Generalized loop super-Virasoro algebras | automorphisms | second cohomology groups | REPRESENTATIONS | HARISH-CHANDRA MODULES | WITT TYPE | INTERMEDIATE SERIES | LIE-ALGEBRAS | MATHEMATICS | WZW MODEL | 2ND COHOMOLOGY | Algebra | Derivation | Mathematical analysis | Automorphisms | Group theory

Journal Article

Bulletin of the Korean Mathematical Society, ISSN 1015-8634, 2016, Volume 53, Issue 6, pp. 1685 - 1695

In this article we consider Lie super-bialgebra structures on the generalized loop super-Virasoro algebra G. By proving that the first cohomology group H-1(G,G...

Generalized loop super-Virasoro algebra | Lie super-bialgebra | Yang-Baxter equation | MATHEMATICS | generalized loop super-Virasoro algebra | MODULES | WITT | INTERMEDIATE SERIES

Generalized loop super-Virasoro algebra | Lie super-bialgebra | Yang-Baxter equation | MATHEMATICS | generalized loop super-Virasoro algebra | MODULES | WITT | INTERMEDIATE SERIES

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 3/2010, Volume 91, Issue 3, pp. 289 - 305

In this article, we prove the classification theorem of the unitarizable highest weight modules over the N = 2 super Virasoro algebras for the untwisted...

Geometry | 17B68 | unitarizable modules | Theoretical, Mathematical and Computational Physics | 17B10 | Group Theory and Generalizations | Statistical Physics, Dynamical Systems and Complexity | N = 2 super Virasoro algebras | Physics | Unitarizable modules | N = 2 super Virasoro algebras | INVARIANCE | UNITARY REPRESENTATIONS | N=2 super Virasoro algebras | SUPERCONFORMAL ALGEBRAS | DETERMINANT FORMULAS | PHYSICS, MATHEMATICAL | 2 DIMENSIONS

Geometry | 17B68 | unitarizable modules | Theoretical, Mathematical and Computational Physics | 17B10 | Group Theory and Generalizations | Statistical Physics, Dynamical Systems and Complexity | N = 2 super Virasoro algebras | Physics | Unitarizable modules | N = 2 super Virasoro algebras | INVARIANCE | UNITARY REPRESENTATIONS | N=2 super Virasoro algebras | SUPERCONFORMAL ALGEBRAS | DETERMINANT FORMULAS | PHYSICS, MATHEMATICAL | 2 DIMENSIONS

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 01/2017, Volume 65, Issue 1, pp. 58 - 66

In this paper, we attempt to investigate the super-biderivations of Lie superalgebras. Furthermore, we prove that all super-biderivations on the centerless...

super-Virasoro algebras | Lie superalgebras | super-biderivations | biderivations | MATHEMATICS | MODULES | VIRASORO ALGEBRA | LINEAR COMMUTING MAPS | Algebra

super-Virasoro algebras | Lie superalgebras | super-biderivations | biderivations | MATHEMATICS | MODULES | VIRASORO ALGEBRA | LINEAR COMMUTING MAPS | Algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 2012, Volume 352, Issue 1, pp. 1 - 61

Divergence-free Lie algebras (also known as the special Lie algebras of Cartan type) are Lie algebras of volume-preserving transformation groups. They are...

Irreducible modules | Graded modules | Divergence-free Lie algebra | Cartan type | Classification | CHARACTERISTIC ZERO | HARISH-CHANDRA MODULES | BLOCK TYPE | IRREDUCIBLE REPRESENTATIONS | INTERMEDIATE SERIES | DERIVATIONS | MATHEMATICS | GENERALIZED WITT ALGEBRAS | SUPER-VIRASORO ALGEBRAS

Irreducible modules | Graded modules | Divergence-free Lie algebra | Cartan type | Classification | CHARACTERISTIC ZERO | HARISH-CHANDRA MODULES | BLOCK TYPE | IRREDUCIBLE REPRESENTATIONS | INTERMEDIATE SERIES | DERIVATIONS | MATHEMATICS | GENERALIZED WITT ALGEBRAS | SUPER-VIRASORO ALGEBRAS

Journal Article

Communications in Algebra, ISSN 0092-7872, 10/2019, Volume 47, Issue 10, pp. 4230 - 4246

In this paper, we determine the first cohomology groups of centerless N = 1 super Virasoro algebras with coefficients in their tensor density modules. As...

super Virasoro algebras | the first cohomology groups | Central extensions | MATHEMATICS | EXTENSIONS | HARISH-CHANDRA MODULES | MODEL | NEVEU-SCHWARZ | Mathematical analysis | Homology | Tensors

super Virasoro algebras | the first cohomology groups | Central extensions | MATHEMATICS | EXTENSIONS | HARISH-CHANDRA MODULES | MODEL | NEVEU-SCHWARZ | Mathematical analysis | Homology | Tensors

Journal Article

Communications in Algebra, ISSN 0092-7872, 12/2017, Volume 45, Issue 12, pp. 5252 - 5261

In this paper, the biderivations without the skew-symmetric condition of W-algebras including the Witt algebra, the algebra W(2,2) and their central extensions...

post-Lie algebra | Biderivation | W-algebra | linear commuting map | TRIANGULAR ALGEBRAS | W(2,2) | SERIES | REPRESENTATIONS | MATHEMATICS | MODULES | MATRICES | AFFINE | SUPER-VIRASORO ALGEBRAS | Quantum theory | Algebra | Lie groups

post-Lie algebra | Biderivation | W-algebra | linear commuting map | TRIANGULAR ALGEBRAS | W(2,2) | SERIES | REPRESENTATIONS | MATHEMATICS | MODULES | MATRICES | AFFINE | SUPER-VIRASORO ALGEBRAS | Quantum theory | Algebra | Lie groups

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 04/2007, Volume 48, Issue 4, pp. 043508 - 043508-15

In this paper, we first discuss the structure of the Ramond N = 2 superconformal algebras. Then we classify the modules of the intermediate series over Ramond...

KAC | PHYSICS, MATHEMATICAL | SUPER-VIRASORO ALGEBRAS | CONJECTURE | Mathematics - Quantum Algebra | CONFORMAL INVARIANCE | CLASSIFICATION | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SUPERSYMMETRY | QUANTUM FIELD THEORY | ALGEBRA

KAC | PHYSICS, MATHEMATICAL | SUPER-VIRASORO ALGEBRAS | CONJECTURE | Mathematics - Quantum Algebra | CONFORMAL INVARIANCE | CLASSIFICATION | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SUPERSYMMETRY | QUANTUM FIELD THEORY | ALGEBRA

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 08/2010, Volume 51, Issue 8, pp. 083513 - 083513-17

In this paper, a classification of indecomposable modules of the intermediate series over the twisted N = 2 superconformal algebra is obtained.

HARISH-CHANDRA MODULES | LIE-ALGEBRA | KAC | PHYSICS, MATHEMATICAL | SUPER-VIRASORO ALGEBRAS | CONJECTURE

HARISH-CHANDRA MODULES | LIE-ALGEBRA | KAC | PHYSICS, MATHEMATICAL | SUPER-VIRASORO ALGEBRAS | CONJECTURE

Journal Article

Algebra Colloquium, ISSN 1005-3867, 06/2013, Volume 20, Issue 2, pp. 269 - 284

In this paper, Lie super-bialgebra structures on generalized Ramond N = 2 super-Virasoro algebras L are determined. It is proved that all Lie super-bialgebras...

Lie super-bialgebras | Yang-Baxter equation | Generalized Ramond N=2 super-Virasoro algebras | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATION-THEORY | generalized Ramond N=2 super-Virasoro algebras | CLASSIFICATION | WITT TYPE | 2 DIMENSIONS

Lie super-bialgebras | Yang-Baxter equation | Generalized Ramond N=2 super-Virasoro algebras | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATION-THEORY | generalized Ramond N=2 super-Virasoro algebras | CLASSIFICATION | WITT TYPE | 2 DIMENSIONS

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 10/2015, Volume 10, Issue 5, pp. 1233 - 1242

There are two extensions of Virasoro algebra with particular importance in superstring theory: the Ramond algebra and the Neveu-Schwarz algebra, which are...

Ramond algebra | Super-Virasoro algebra | 17B68 | weight module | 17B10 | 17B65 | Mathematics, general | Mathematics | Harish-Chandra module | MATHEMATICS | REPRESENTATIONS | HARISH-CHANDRA MODULES | CONJECTURE | Studies | Algebra | Mathematical analysis | Classification

Ramond algebra | Super-Virasoro algebra | 17B68 | weight module | 17B10 | 17B65 | Mathematics, general | Mathematics | Harish-Chandra module | MATHEMATICS | REPRESENTATIONS | HARISH-CHANDRA MODULES | CONJECTURE | Studies | Algebra | Mathematical analysis | Classification

Journal Article

数学物理学报：B辑英文版, ISSN 0252-9602, 2010, Volume 30, Issue 1, pp. 225 - 239

In this article, Lie super-bialgebra structures on generalized super-Virasoro algebras/： are considered. It is proved that all such Lie super-bialgebras are...

三角 | 广义 | 谎言 | 双代数 | 代数结构 | 超代数 | generalized super-Virasoro algebras | 17B66 | Yang-Baxter equation | 17B62 | 17B37 | Lie super-bialgebras | 17B05 | MATHEMATICS | HARISH-CHANDRA MODULES | CLASSIFICATION | WITT | Scripts | Operators | Algebra

三角 | 广义 | 谎言 | 双代数 | 代数结构 | 超代数 | generalized super-Virasoro algebras | 17B66 | Yang-Baxter equation | 17B62 | 17B37 | Lie super-bialgebras | 17B05 | MATHEMATICS | HARISH-CHANDRA MODULES | CLASSIFICATION | WITT | Scripts | Operators | Algebra

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 03/2008, Volume 235, Issue 1, pp. 43 - 55

We classify the compatible left-symmetric superalgebraic structures on the super-Virasoro algebras satisfying certain natural conditions.

Virasoro algebra | Super-Virasoro algebra | Left-symmetric superalgebra | LIE-ALGEBRAS | MATHEMATICS | YANG-BAXTER EQUATION | MATRIX | PIONS | DOUBLE EXTENSION | left-symmetric superalgebra | ABELIAN PHASE SPACES | super-Virasoro algebra | MODEL | AFFINE GEOMETRY

Virasoro algebra | Super-Virasoro algebra | Left-symmetric superalgebra | LIE-ALGEBRAS | MATHEMATICS | YANG-BAXTER EQUATION | MATRIX | PIONS | DOUBLE EXTENSION | left-symmetric superalgebra | ABELIAN PHASE SPACES | super-Virasoro algebra | MODEL | AFFINE GEOMETRY

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 2007, Volume 211, Issue 3, pp. 596 - 608

Let B be the universal central extension of a graded Lie algebra of Block type. In this paper, it is proved that any quasifinite irreducible B -module is...

MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | HARISH-CHANDRA MODULES | CLASSIFICATION | INTERMEDIATE SERIES | SUPER-VIRASORO ALGEBRAS

MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | HARISH-CHANDRA MODULES | CLASSIFICATION | INTERMEDIATE SERIES | SUPER-VIRASORO ALGEBRAS

Journal Article

Communications in Algebra, ISSN 0092-7872, 12/2016, Volume 44, Issue 12, pp. 5342 - 5350

Let SVir be the well-known super-Virasoro algebras. In this paper, we first prove that any super-skewsymmetric super-biderivation of SVir is inner. Based on...

Super-commuting maps | Super-Virasoro algebras | Super-biderivations | MATHEMATICS | Charge | Mapping | Algebra | Maps

Super-commuting maps | Super-Virasoro algebras | Super-biderivations | MATHEMATICS | Charge | Mapping | Algebra | Maps

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2004, Volume 214, Issue 2, pp. 450 - 518

In this article, we study the structure of Verma modules and Fock modules over the twisted sector of the N=2 super Virasoro algebras.

Verma modules | N=2 super Virasoro algebras | Fock modules | Jantzen filtration | N = 2 super Virasoro algebras | MATHEMATICS | MODULES | NEVEU-SCHWARZ

Verma modules | N=2 super Virasoro algebras | Fock modules | Jantzen filtration | N = 2 super Virasoro algebras | MATHEMATICS | MODULES | NEVEU-SCHWARZ

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 6/2009, Volume 4, Issue 2, pp. 365 - 379

In this paper we obtain that every super-Virasoro algebra admits only triangular coboundary Lie super-bialgebra structures and this is proved mainly based on...

17B66 | Yang-Baxter equation | Lie super-bialgebra | 17B62 | Mathematics, general | super-Virasoro algebra | Mathematics | 17B37 | 17B05 | Super-Virasoro algebra | MATHEMATICS | HARISH-CHANDRA MODULES | CLASSIFICATION | WITT | Studies | Algebra | Lie groups

17B66 | Yang-Baxter equation | Lie super-bialgebra | 17B62 | Mathematics, general | super-Virasoro algebra | Mathematics | 17B37 | 17B05 | Super-Virasoro algebra | MATHEMATICS | HARISH-CHANDRA MODULES | CLASSIFICATION | WITT | Studies | Algebra | Lie groups

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 10/2006, Volume 78, Issue 1, pp. 89 - 96

In this note, we determine the structure of the pre-Verma modules $$N(z,\frac{1}{24}z)$$ over the N = 1 Ramond algebra. The results of this note together with...

Geometry | Ramond algebra | N = 1 super Virasoro algebra | Verma module | 17B68 | Mathematical and Computational Physics | 17B10 | the Jantzen filtration | Group Theory and Generalizations | Physics | Statistical Physics | The Jantzen filtration | N =1 super Virasoro algebra | N=1 super Virasoro algebra | REPRESENTATION-THEORY | PHYSICS, MATHEMATICAL | NEVEU-SCHWARZ

Geometry | Ramond algebra | N = 1 super Virasoro algebra | Verma module | 17B68 | Mathematical and Computational Physics | 17B10 | the Jantzen filtration | Group Theory and Generalizations | Physics | Statistical Physics | The Jantzen filtration | N =1 super Virasoro algebra | N=1 super Virasoro algebra | REPRESENTATION-THEORY | PHYSICS, MATHEMATICAL | NEVEU-SCHWARZ

Journal Article

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