Vertex Operator Construction for the Toroidal Lie Algebra of TypeF4

2003 ◽  
Vol 31 (5) ◽  
pp. 2161-2182 ◽  
Author(s):  
Hong You ◽  
Cuipo Jiang
Keyword(s):  
Lie Algebra ◽  
Vertex Operator ◽  
Toroidal Lie Algebra ◽  
Operator Construction

scholarly journals Combinatorial bases of modules for affine Lie algebra B 2(1)

2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Mirko Primc
Keyword(s):  
Lie Algebra ◽  
Vertex Operator ◽  
Vertex Operator Algebra ◽  
Intertwining Operators ◽  
Type B ◽  
Highest Weight Module ◽  
Highest Weight ◽  
Affine Lie Algebra ◽  
Algebra Theory ◽  
Simple Currents

AbstractWe construct bases of standard (i.e. integrable highest weight) modules L(Λ) for affine Lie algebra of type B 2(1) consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces W(Λ) of L(Λ) by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence W(kΛ0) for B 2(1) and the integrable highest weight module L(kΛ0) for A 1(1) have the same parametrization of combinatorial bases and the same presentation P/I.

scholarly journals Fermionic realization of twisted toroidal Lie algebras

2020 ◽  
pp. 2150143
Author(s):  
Naihuan Jing ◽  
Chad R. Mangum ◽  
Kailash C. Misra
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Type Formula ◽  
Toroidal Lie Algebra

In this paper, we construct a fermionic realization of the twisted toroidal Lie algebra of type [Formula: see text] and [Formula: see text] based on the newly found Moody–Rao–Yokonuma-like presentation.

scholarly journals A note on the zeroth products of Frenkel–Jing operators

2017 ◽  
Vol 16 (03) ◽  
pp. 1750053 ◽  
Author(s):  
Slaven Kožić
Keyword(s):  
Lie Algebra ◽  
Vertex Operator ◽  
Vertex Operator Algebra ◽  
Vertex Algebra ◽  
Infinite Dimensional ◽  
Enveloping Algebra ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Quantum Vertex ◽  
Algebra Theory

Let [Formula: see text] be an untwisted affine Kac–Moody Lie algebra. The top of every irreducible highest weight integrable [Formula: see text]-module is the finite-dimensional irreducible [Formula: see text]-module, where the action of the simple Lie algebra [Formula: see text] is given by zeroth products arising from the underlying vertex operator algebra theory. Motivated by this fact, we consider zeroth products of level [Formula: see text] Frenkel–Jing operators corresponding to Drinfeld realization of the quantum affine algebra [Formula: see text]. By applying these products, which originate from the quantum vertex algebra theory developed by Li, on the extension of Koyama vertex operator [Formula: see text], we obtain an infinite-dimensional vector space [Formula: see text]. Next, we introduce an associative algebra [Formula: see text], a certain quantum analogue of the universal enveloping algebra [Formula: see text], and construct some infinite-dimensional [Formula: see text]-modules [Formula: see text] corresponding to the finite-dimensional irreducible [Formula: see text]-modules [Formula: see text]. We show that the space [Formula: see text] carries a structure of an [Formula: see text]-module and, furthermore, we prove that the [Formula: see text]-module [Formula: see text] is isomorphic to the [Formula: see text]-module [Formula: see text].

scholarly journals Vertex Representations for the ν+1-Toroidal Lie Algebra of Type Bl

2001 ◽  
Vol 246 (2) ◽  
pp. 564-593 ◽  
Author(s):  
Jiang Cuipo ◽  
Meng Daoji
Keyword(s):  
Lie Algebra ◽  
Toroidal Lie Algebra

scholarly journals Uprolling unrolled quantum groups

2021 ◽  
pp. 2150023
Author(s):  
Thomas Creutzig ◽  
Matthew Rupert
Keyword(s):  
Quantum Group ◽  
Lie Algebra ◽  
Quantum Groups ◽  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Algebra ◽  
Vertex Operator Algebras ◽  
Roots Of Unity ◽  
Simple Lie Algebra ◽  
Higher Rank

We construct families of commutative (super) algebra objects in the category of weight modules for the unrolled restricted quantum group [Formula: see text] of a simple Lie algebra [Formula: see text] at roots of unity, and study their categories of local modules. We determine their simple modules and derive conditions for these categories being finite, non-degenerate, and ribbon. Motivated by numerous examples in the [Formula: see text] case, we expect some of these categories to compare nicely to categories of modules for vertex operator algebras. We focus in particular on examples expected to correspond to the higher rank triplet vertex algebra [Formula: see text] of Feigin and Tipunin and the [Formula: see text] algebras.

scholarly journals On orbifold constructions associated with the Leech lattice vertex operator algebra

2018 ◽  
Vol 168 (2) ◽  
pp. 261-285 ◽  
Author(s):  
CHING HUNG LAM ◽  
HIROKI SHIMAKURA
Keyword(s):  
Lie Algebra ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Central Charge ◽  
Leech Lattice ◽  
Weight One ◽  
Strongly Regular ◽  
Lattice Vertex Operator Algebra

AbstractIn this paper, we study orbifold constructions associated with the Leech lattice vertex operator algebra. As an application, we prove that the structure of a strongly regular holomorphic vertex operator algebra of central charge 24 is uniquely determined by its weight one Lie algebra if the Lie algebra has the type A3,43A1,2, A4,52, D4,12A2,6, A6,7, A7,4A1,13, D5,8A1,2 or D6,5A1,12 by using the reverse orbifold construction. Our result also provides alternative constructions of these vertex operator algebras (except for the case A6,7) from the Leech lattice vertex operator algebra.

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