1,721,107 research outputs found
Essential Variational Poisson Cohomology
Full text linkIn our recent paper "The variational Poisson cohomology" (2011) we computed the dimension of the variational Poisson cohomology for any quasiconstant coefficient a" x a" matrix differential operator K of order N with invertible leading coefficient, provided that is a normal algebra of differential functions over a linearly closed differential field. In the present paper we show that, for K skewadjoint, the -graded Lie superalgebra is isomorphic to the finite dimensional Lie superalgebra . We also prove that the subalgebra of "essential" variational Poisson cohomology, consisting of classes vanishing on the Casimirs of K, is zero. This vanishing result has applications to the theory of bi-Hamiltonian structures and their deformations. At the end of the paper we consider also the translation invariant case
Classical affine W -Algebras for glN and associated integrable Hamiltonian hierarchies
Full text linkWe apply the new method for constructing integrable Hamiltonian hierarchies of Lax type equations developed in our previous paper to show that all W-algebras W(,) carry such a hierarchy. As an application, we show that all vector constrained KP hierarchies and their matrix generalizations are obtained from these hierarchies by Dirac reduction, which provides the former with a bi-Poisson structure
Algebraic vs physical N = 6 3-algebras
No full textIn our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories
Finite vs infinite decompositions in conformal embeddings
Full text linkBuilding on work of the first and last author, we prove that an embedding of simple affine vertex algebras , corresponding to an embedding of a maximal equal rank reductive subalgebra into a simple Lie algebra , is conformal if and only if the corresponding central charges are equal. We classify the equal rank conformal embeddings. Furthermore we describe, in almost all cases, when decomposes finitely as a -module
Addendum: Generalized Spencer cohomology and filtered deformations of -graded Lie superalgebras""
No full textClassification of Linearly Compact Simple Rigid Superalgebras
No full textThe notion of an anti-commutative (resp. commutative) rigid superalgebra is a natural generalization of the notion of a Lie (resp. Jordan) superalgebra. Intuitively, rigidity means that small deformations of the product under the action of the structural group produce an isomorphic algebra. In this paper, we classify all linearly compact simple anti-commutative (resp. commutative) rigid superalgebras. Beyond Lie (resp. Jordan) superalgebras, the complete list includes four series and 22 exceptional superalgebras (resp. 10 exceptional superalgebras)
REPRESENTATIONS OF AFFINE SUPERALGEBRAS AND MOCK THETA FUNCTIONS
No full textWe show that the normalized supercharacters of principal admissible modules over the affine Lie superalgebra sℓˆ[subscript 2|1] (resp. psℓˆ[subscript 2|2]) can be modified, using Zwegers’ real analytic corrections, to form a modular (resp. S-) invariant family of functions. Applying the quantum Hamiltonian reduction, this leads to a new family of positive energy modules over the N = 2 (resp.N = 4) superconformal algebras with central charge 3(1 − (2 m + 2)/M), where m ∈ ℤ[subscript ≥0], M ∈ ℤ[subscript ≥2], gcd(2 m + 2, M) = 1 if m > 0 (resp. 6 (m/M − 1), where m ∈ ℤ[subscript ≥1], M ∈ ℤ[subscript ≥2], gcd(2 m, M) = 1 if m > 1), whose modified characters and supercharacters form a modular invariant family
Algebraic vs physical N = 6 3-algebras
Full text linkIn our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their "physical" counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories
Classification of linearly compact simple algebraic N = 6 3-algebras
No full textN ≤ 8 3-algebras have recently appeared in N-supersymmetric 3-dimensional Chern-Simons gauge theories. In our previous paper we classified linearly compact simple N = 8 n-algebras for any n ≥ 3. In the present paper we classify algebraic linearly compact simple N = 6 3-algebras over an algebraically closed field of characteristic 0, using their correspondence with simple linearly compact Lie superalgebras with a consistent short ℤ-grading, endowed with a graded conjugation. We also briey discuss N = 5 3-algebras
Representations of superconformal algebras and mock theta functions
Full text linkIt is well known that the normalized characters of integrable highest
weight modules of given level over an affine Lie algebra [care over g] span an SL[subscript 2](Z)-invariant space. This result extends to admissible [caret over g]-modules, where g is a simple Lie algebra or osp[subscript 1|n]. Applying the quantum Hamiltonian reduction (QHR) to admissible [caret over g]-modules when g = sl[subscript 2] (resp. = osp[subscript 1|2]) one obtains minimal series modules over the Virasoro (resp. N = 1 superconformal algebras), which form modular invariant
families. Another instance of modular invariance occurs for boundary level admissible modules, including when g is a basic Lie superalgebra. For example, if g = sl[subscript 2|1] (resp. = osp[subscript 3|2]), we thus obtain modular invariant families of g-modules, whose QHR produces the minimal series modules for the N = 2 superconformal algebras (resp. a modular invariant family of N = 3 superconformal algebra modules).
However, in the case when g is a basic Lie superalgebra different from a simple Lie algebra or osp[subscript 1|n], modular invariance of normalized supercharacters of admissible [caret over g]-modules holds outside of boundary levels only after their modification in the spirit
of Zwegers’ modification of mock theta functions. Applying the QHR, we obtain families of representations of N = 2, 3, 4 and big N = 4 superconformal algebras, whose modified (super)characters span an SL[subscript 2](Z)-invariant space
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