1,721,004 research outputs found
Automorphisms and forms of simple infinite-dimensional linearly compact Lie superalgebras
No full textWe describe the group of continuous automorphisms of all simple infinite-dimensional linearly compact Lie superalgebras and use it in order to classify F-forms of these superalgebras over any field F of characteristic zero
Poisson Λ-brackets for Differential-Difference Equations
No full textWe introduce the notion of a multiplicative Poisson λ-bracket, which plays the same role in the theory of Hamiltonian differential-difference equations as the usual Poisson λ-bracket plays in the theory of Hamiltonian partial differential equations (PDE). We classify multiplicative Poisson λ-brackets in one difference variable up to order 5. As an example, we demonstrate how to apply the Lenard-Magri scheme to a compatible pair of multiplicative Poisson λ-brackets of order 1 and 2, to establish integrability of the Volterra chain
Corrigendum to “Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting” (Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting (2008) 217(6) (2485–2562), (S0001870807003088), (10.1016/j.aim.2007.10.005))
No full textInfinite dimensional primitive linearly compact Lie superalgebras
No full textWe classify open maximal subalgebras of all infinite-dimensional linearly compact simple Lie superalgebras. This is applied to the classification of infinite-dimensional Lie superalgebras of vector fields, acting transitively and primitively in a formal neighborhood of a point of a finite-dimensional supermanifold
Chiral versus classical operad
No full textWe establish an explicit isomorphism between the associated graded of the filtered chiral operad and the classical operad, which is important for computing the cohomology of vertex algebras
On Lax operators
Full text linkWe define a Lax operator as a monic pseudodifferential operator L(∂) of order N ≥ 1, such that the Lax equations ∂L(∂)∂tk=[(L_k^N(∂))_+,L(∂)] are consistent and non-zero for infinitely many positive integers k. Consistency of an equation means that its flow is defined by an evolutionary vector field. In the present paper we demonstrate that the traditional theory of the KP and the N-th KdV hierarchies holds for arbitrary scalar Lax operators
An operadic approach to vertex algebra and Poisson vertex algebra cohomology
No full textWe translate the construction of the chiral operad by Beilinson and Drinfeld to the purely algebraic language of vertex algebras. Consequently, the general construction of a cohomology complex associated to a linear operad produces the vertex algebra cohomology complex. Likewise, the associated graded of the chiral operad leads to the classical operad, which produces a Poisson vertex algebra cohomology complex. The latter is closely related to the variational Poisson cohomology studied by two of the authors
Classification 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)
Computation of cohomology of vertex algebras
Full text linkWe review cohomology theories corresponding to the chiral and classical operads. The first one is the cohomology theory of vertex algebras, while the second one is the classical cohomology of Poisson vertex algebras (PVA), and we construct a spectral sequence relating them. Since in “good” cases the classical PVA cohomology coincides with the variational PVA cohomology and there are well-developed methods to compute the latter, this enables us to compute the cohomology of vertex algebras in many interesting cases. Finally, we describe a unified approach to integrability through vanishing of the first cohomology, which is applicable to both classical and quantum systems of Hamiltonian PDEs
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