2011, Contemporary mathematics, ISBN 9780821852392, Volume 537, viii, 324

Book

Advances in Mathematics, ISSN 0001-8708, 03/2020, Volume 363, p. 106985

In this paper, we explore natural connections among trigonometric Lie algebras, (general) affine Lie algebras, and vertex algebras. Among the main results, we...

Affine Lie algebras | Vertex algebras | Trigonometric Lie algebras | MATHEMATICS | QUASI-MODULES | REPRESENTATIONS | OPERATOR-ALGEBRAS

Affine Lie algebras | Vertex algebras | Trigonometric Lie algebras | MATHEMATICS | QUASI-MODULES | REPRESENTATIONS | OPERATOR-ALGEBRAS

Journal Article

Journal of Algebra, ISSN 0021-8693, 02/2014, Volume 399, pp. 1086 - 1106

In this paper, we present a canonical association of quantum vertex algebras and their ϕ-coordinated modules to Lie algebra gl∞ and its 1-dimensional central...

Quantum vertex algebra | ϕ-coordinated module | Infinite-dimensional general Lie algebra | φ-coordinated module | phi-coordinated module | MATHEMATICS | REPRESENTATIONS | W1+INFINITY | SOLITON-EQUATIONS | OPERATORS | TRANSFORMATION GROUPS | Algebra

Quantum vertex algebra | ϕ-coordinated module | Infinite-dimensional general Lie algebra | φ-coordinated module | phi-coordinated module | MATHEMATICS | REPRESENTATIONS | W1+INFINITY | SOLITON-EQUATIONS | OPERATORS | TRANSFORMATION GROUPS | Algebra

Journal Article

2013, 2nd ed., Advanced series in mathematical physics, ISBN 9814522198, Volume 29, xii, 237

Book

Journal of Algebra, ISSN 0021-8693, 09/2019, Volume 534, pp. 168 - 189

In this paper, we introduce an infinite-dimensional Lie algebra DS for any abelian group S. If S is the additive group of integers, DS reduces to the...

Vertex algebras | Affine Kac-Moody Lie algebras | q-Virasoro algebra | MATHEMATICS

Vertex algebras | Affine Kac-Moody Lie algebras | q-Virasoro algebra | MATHEMATICS

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 03/2020, Volume 224, Issue 3, pp. 1241 - 1279

In this paper, a holomorphic vertex operator algebra U of central charge 24 with the weight one Lie algebra A8,3A2,12 is proved to be unique. Moreover, a...

Simple Lie algebra | Holomorphic vertex operator algebra

Simple Lie algebra | Holomorphic vertex operator algebra

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2019, Volume 21, Issue 8, p. 1850069

We construct three families of vertex algebras along with their modules from appropriate vertex Lie algebras, using the constructions in [Vertex Lie algebra,...

Bakas-Block algebra | vertex Lie algebra | polynomial Virasoro algebra | vertex tensor category | β γ -system | Strongly graded vertex algebra | C 1 A -cofiniteness condition | INVARIANCE | MATHEMATICS, APPLIED | REPRESENTATIONS | EQUATIONS | MATHEMATICS | C-1(A)-cofiniteness condition | SYSTEMS | QUASIFINITE MODULES | beta gamma-system | Algebra

Bakas-Block algebra | vertex Lie algebra | polynomial Virasoro algebra | vertex tensor category | β γ -system | Strongly graded vertex algebra | C 1 A -cofiniteness condition | INVARIANCE | MATHEMATICS, APPLIED | REPRESENTATIONS | EQUATIONS | MATHEMATICS | C-1(A)-cofiniteness condition | SYSTEMS | QUASIFINITE MODULES | beta gamma-system | Algebra

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 9/2018, Volume 362, Issue 3, pp. 827 - 854

Using the tensor category theory developed by Lepowsky, Zhang and the second author, we construct a braided tensor category structure with a twist on a...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | DIMENSIONS | COHOMOLOGY | FUSION RULES | INVARIANT REPRESENTATIONS | MODELS | FIELD-THEORY | VERLINDE FORMULAS | VERTEX OPERATOR-ALGEBRAS | FRACTIONAL LEVEL | PRODUCT THEORY | PHYSICS, MATHEMATICAL | Algebra | Mathematics - Quantum Algebra

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | DIMENSIONS | COHOMOLOGY | FUSION RULES | INVARIANT REPRESENTATIONS | MODELS | FIELD-THEORY | VERLINDE FORMULAS | VERTEX OPERATOR-ALGEBRAS | FRACTIONAL LEVEL | PRODUCT THEORY | PHYSICS, MATHEMATICAL | Algebra | Mathematics - Quantum Algebra

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 12/2016, Volume 110, pp. 176 - 186

In this paper, we study a class of infinite-dimensional Lie algebras generalizing the constant r-term Krichever–Novikov type algebras. We associate vertex...

Vertex algebras | Lie algebras of Krichever–Novikov type | Modules | 2 POINTS | MATHEMATICS, APPLIED | Lie algebras of Krichever-Novikov type | PHYSICS, MATHEMATICAL | OPERATORS | Algebra

Vertex algebras | Lie algebras of Krichever–Novikov type | Modules | 2 POINTS | MATHEMATICS, APPLIED | Lie algebras of Krichever-Novikov type | PHYSICS, MATHEMATICAL | OPERATORS | Algebra

Journal Article

1988, Advanced series in mathematical physics, ISBN 9789971504199, Volume 3, xiii, 586

Book

Communications in Algebra, ISSN 0092-7872, 01/2017, Volume 45, Issue 1, pp. 141 - 150

In this paper, simplicity of quadratic Lie conformal algebras is investigated. From the view point of the corresponding Gel'fand-Dorfman bialgebras, some...

Lie conformal algebra | Gel'fand-Dorfman bialgebra | infinite-dimensional Lie algebra | Novikov algebra | Novikov-Jordan algebra | Novikov–Jordan algebra | Gel’fand–Dorfman bialgebra | GC(N) | CHARACTERISTIC-0 | CLASSIFICATION | VERTEX ALGEBRAS | MATHEMATICS | COHOMOLOGY | NOVIKOV ALGEBRAS | SUPERALGEBRAS | Algebra | Classification

Lie conformal algebra | Gel'fand-Dorfman bialgebra | infinite-dimensional Lie algebra | Novikov algebra | Novikov-Jordan algebra | Novikov–Jordan algebra | Gel’fand–Dorfman bialgebra | GC(N) | CHARACTERISTIC-0 | CLASSIFICATION | VERTEX ALGEBRAS | MATHEMATICS | COHOMOLOGY | NOVIKOV ALGEBRAS | SUPERALGEBRAS | Algebra | Classification

Journal Article

2017, Volume 695.

Category theory; homological algebra | Lie algebras | Vertex operators; vertex operator algebras and related structures | Axiomatic quantum field theory; operator algebras | Quantum field theory; related classical field theories | Lie algebras and Lie superalgebras | Several complex variables and analytic spaces | Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories | Vertex operator algebras | Lie algebras of linear algebraic groups | Categories with structure | Moduli of Riemann surfaces, Teichm | Nonassociative rings and algebras | Deformations of analytic structures | Quantum theory | Representations of algebras

Conference Proceeding

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 09/2017, Volume 50, Issue 40, p. 404002

We give a new, simpler proof that the canonical actions of finite groups on Fricke-type Monstrous Lie algebras yield genus zero functions in generalized...

vertex operator algebra | MODULE | GENERALIZED MOONSHINE | PHYSICS, MULTIDISCIPLINARY | Hauptmodul | Monstrous Moonshine | Borcherds-Kac-Moody Lie algebras | PHYSICS, MATHEMATICAL

vertex operator algebra | MODULE | GENERALIZED MOONSHINE | PHYSICS, MULTIDISCIPLINARY | Hauptmodul | Monstrous Moonshine | Borcherds-Kac-Moody Lie algebras | PHYSICS, MATHEMATICAL

Journal Article

2012, Volume 584

Conference Proceeding

Journal of Algebra, ISSN 0021-8693, 02/2015, Volume 424, pp. 126 - 146

In this paper, we associate vertex algebras and their two different kinds of module categories with the unitary Lie algebra uˆN(CΓ˜) for N≥2 being a positive...

Vertex algebras | Unitary Lie algebra | MATHEMATICS | AFFINE | Algebra

Vertex algebras | Unitary Lie algebra | MATHEMATICS | AFFINE | Algebra

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2014, Volume 264, pp. 261 - 295

We study Zhu's algebra, C2-algebra and C2-cofiniteness of parafermion vertex operator algebras. We first give a detailed study of Zhu's algebra and C2-algebra...

Affine Lie algebras | Vertex operator algebras | Affine lie algebras

Affine Lie algebras | Vertex operator algebras | Affine lie algebras

Journal Article

Journal of Algebra, ISSN 0021-8693, 08/2017, Volume 484, pp. 88 - 108

In this paper, we prove that the categories of lower bounded twisted modules of positive integer levels for simple vertex operator algebras associated with...

Affine Lie algebras | Vertex operator algebras | Twisted Zhu's algebras | Logarithmic twisted modules | MATHEMATICS | Algebra

Affine Lie algebras | Vertex operator algebras | Twisted Zhu's algebras | Logarithmic twisted modules | MATHEMATICS | Algebra

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 04/2017, Volume 19, Issue 2, p. 1650015

Given a vertex Lie algebra ℒ equipped with an action by automorphisms of a cyclic group Γ , we define spaces of cyclotomic coinvariants over the Riemann...

Vertex algebras | Vertex Lie algebras | Cyclotomic coinvariants | Infinite dimensional Lie algebras | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | cyclotomic coinvariants | MODEL | vertex Lie algebras | infinite dimensional Lie algebras | Algebra | Mathematics - Quantum Algebra

Vertex algebras | Vertex Lie algebras | Cyclotomic coinvariants | Infinite dimensional Lie algebras | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | cyclotomic coinvariants | MODEL | vertex Lie algebras | infinite dimensional Lie algebras | Algebra | Mathematics - Quantum Algebra

Journal Article

Journal of Noncommutative Geometry, ISSN 1661-6952, 2012, Volume 6, Issue 3, pp. 539 - 602

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy...

Batalin-Vilkovisky algebra | Vertex algebras | Topological conformal field theory | Homotopy algebras | Koszul duality theory | Gerstenhaber algebra | Framed little disc | Maurer-Cartan equation | Operad | OPERADS | HIGHER DERIVED BRACKETS | MATHEMATICS, APPLIED | vertex algebras | REPRESENTATIONS | FIELD-THEORIES | operad framed little disc | PHYSICS, MATHEMATICAL | DEFORMATION-THEORY | MATHEMATICS | PRODUCTS | KOSZUL DUALITY | HOCHSCHILD COHOMOLOGY | topological conformal field theory | homotopy algebras | CHIRAL DIFFERENTIAL-OPERATORS | DELIGNE CONJECTURE

Batalin-Vilkovisky algebra | Vertex algebras | Topological conformal field theory | Homotopy algebras | Koszul duality theory | Gerstenhaber algebra | Framed little disc | Maurer-Cartan equation | Operad | OPERADS | HIGHER DERIVED BRACKETS | MATHEMATICS, APPLIED | vertex algebras | REPRESENTATIONS | FIELD-THEORIES | operad framed little disc | PHYSICS, MATHEMATICAL | DEFORMATION-THEORY | MATHEMATICS | PRODUCTS | KOSZUL DUALITY | HOCHSCHILD COHOMOLOGY | topological conformal field theory | homotopy algebras | CHIRAL DIFFERENTIAL-OPERATORS | DELIGNE CONJECTURE

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 11/2016, Volume 106, Issue 11, pp. 1575 - 1585

Journal Article

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