Unifying W-algebras

Blumenhagen, Ralph; Eholzer, Wolfgang; Honecker, A.; Hornfeck, K.; Hübel, R.

doi:10.1016/0370-2693(94)90857-5

Cited by 33 publications

(70 citation statements)

References 37 publications

(74 reference statements)

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“…The identification (3.24) is further supported by explicit calculations presented in detail in [22]. The energy momentum tensor of the quantum coset is just the normal ordered version of (3.20a).…”

Section: On General Cosets and The Deformable W(2 3 4 5)-algebramentioning

confidence: 64%

“…Because the above contradicts an earlier claim [10], we wish to draw the reader's attention to the further evidence in [22], which shows that the claim of [10] that the quantum coset sl(2) k / U (1) requires infinitely many generators (one for each integer scale dimension greater than or equal to two) is incorrect as it stands. First, it can be shown [22] that sl(2) k / U (1) is isomorphic to SVIR(N = 2)/ U (1), which we have argued here to be finitely generated.…”

Section: On General Cosets and The Deformable W(2 3 4 5)-algebramentioning

confidence: 84%

“…It is straightforward to make an ansatz in the uncharged fields and determine those linear combinations that commute with the complete current. One finds precisely one new generator at scale dimensions 3, 4 and 5 with leading terms quadratic in the fermions G ± , and by computing the OPEs of these composite fields one recovers [22] the structure constants of the W(2, 3, 4, 5) given in [8].…”

Section: On General Cosets and The Deformable W(2 3 4 5)-algebramentioning

confidence: 99%

“…In fact, the coset algebra (3.24) is a universal object [22] for the first unitary minimal models of the Casimir algebras based on A k−1 which describe the Z Z k -parafermions [24,25]. Moreover, it is also well known (see e.g.…”

Section: On General Cosets and The Deformable W(2 3 4 5)-algebramentioning

confidence: 99%

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A class of -algebras with infinitely generated classical limit

1994

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There is a relatively well understood class of deformable W-algebras, resulting from Drinfeld-Sokolov (DS) type reductions of Kac-Moody algebras, which are Poisson bracket algebras based on finitely, freely generated rings of differential polynomials in the classical limit. The purpose of this paper is to point out the existence of a second class of deformable W-algebras, which in the classical limit are Poisson bracket algebras carried by infinitely, nonfreely generated rings of differential polynomials. We present illustrative examples of coset constructions, orbifold projections, as well as first class Hamiltonian reductions of DS type W-algebras leading to reduced algebras with such infinitely generated classical limit. We also show in examples that the reduced quantum algebras are finitely generated due to quantum corrections arising upon normal ordering the relations obeyed by the classical generators. We apply invariant theory to describe the relations and to argue that classical cosets are infinitely, nonfreely generated in general. As a by-product, we also explain the origin of the previously constructed and so far unexplained deformable quantum W(2, 4, 6) and W(2, 3, 4, 5) algebras.

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Section: On General Cosets and The Deformable W(2 3 4 5)-algebramentioning

confidence: 64%

Section: On General Cosets and The Deformable W(2 3 4 5)-algebramentioning

confidence: 84%

Section: On General Cosets and The Deformable W(2 3 4 5)-algebramentioning

confidence: 99%

Section: On General Cosets and The Deformable W(2 3 4 5)-algebramentioning

confidence: 99%

See 2 more Smart Citations

A class of -algebras with infinitely generated classical limit

1994

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“…(3) Several times during these lectures I have mentioned that there are a large number of possible identifications between W-algebras which occur for specific c values. The most systematic investigation of these identifications have been carried out by Blumenhagen et al and by Hornfeck in [8,9,[39][40][41]. During this work they also uncovered a large class of W-algebras which are not freely generated, i.e.…”

Section: Discussionmentioning

confidence: 95%

W-algebras and their representations

Watts

Conformal Field Theories and Integrable Models

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Quasifinite Representations of Classical Lie Subalgebras of 1+∞

Kač¹,

Wang²,

Yan³

1998

Advances in Mathematics

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We show that there are precisely two, up to conjugation, anti-involutions _ \ of the algebra of differential operators on the circle preserving the principal gradation. We classify the irreducible quasifinite highest weight representations of the central extension D \ of the Lie subalgebra of this algebra fixed by &_ \ , and find the unitary ones. We realize them in terms of highest weight representations of the central extension of the Lie algebra of infinite matrices with finitely many non-zero diagonals over the algebra C[u]Â(u m+1 ) and its classical Lie subalgebras of B, C and D types. Character formulas for positive primitive representations of D \ (including all the unitary ones) are obtained. We also realize a class of primitive representations of D \ in terms of free fields and establish a number of duality results between these primitive representations and finite-dimensional irreducible representations of finitedimensional Lie groups and supergroups. We show that the vacuum module V c of D + carries a vertex algebra structure and establish a relationship between V c for c # 1 2 Z and W-algebras. Academic Press

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Unifying W-algebras

Cited by 33 publications

References 37 publications

A class of -algebras with infinitely generated classical limit

A class of -algebras with infinitely generated classical limit

W-algebras and their representations

Quasifinite Representations of Classical Lie Subalgebras of 1+∞

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