30 research outputs found
Infinite dimensional primitive linearly compact Lie superalgebras
We 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.Comment: 99 page
Classification of linearly compact simple Nambu-Poisson algebras
We introduce the notion of universal odd generalized Poisson superalgebra
associated to an associative algebra A, by generalizing a construction made in
[5]. By making use of this notion we give a complete classification of simple
linearly compact (generalized) n-Nambu-Poisson algebras over an algebraically
closed field of characteristic zero.Comment: 22 page
Classification of simple linearly compact Kantor triple systems over the complex numbers
Simple finite dimensional Kantor triple systems over the complex numbers are
classified in terms of Satake diagrams. We prove that every simple and linearly
compact Kantor triple system has finite dimension and give an explicit
presentation of all the classical and exceptional systems.Comment: 46 pages, 3 tables; v2: Major revision of the introduction; v3: Final
version to appear in Journal of Algebr
Classification of linearly compact simple Nambu-Poisson algebras
We introduce the notion of a universal odd generalized Poisson superalgebra associated with an associative algebra A, by generalizing a construction made in the work of De Sole and Kac [Jpn. J. Math. 8, 1-145 (2013)]. By making use of this notion we give a complete classification of simple linearly compact (generalized) n-Nambu-Poisson algebras over an algebraically closed field of characteristic zero
Algebraic vs physical N = 6 3-algebras
In 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
Automorphisms and forms of simple infinite-dimensional linearly compact Lie superalgebras
We 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.Comment: 24 page
Lie conformal superalgebras and duality of modules over linearly compact Lie superalgebras
We construct a duality functor on the category of continuous representations
of linearly compact Lie superalgebras, using representation theory of Lie
conformal superalgebras. We compute the dual representations of the generalized
Verma modules.Comment: 36 page
Classification of simple linearly compact n-Lie superalgebras
We classify simple linearly compact n-Lie superalgebras with n>2 over a field
F of characteristic 0. The classification is based on a bijective
correspondence between non-abelian n-Lie superalgebras and transitive Z-graded
Lie superalgebras of the form L=\oplus_{j=-1}^{n-1} L_j, such that L_{-1}=g,
where dim L_{n-1}=1, L_{-1} and L_{n-1} generate L, and [L_j, L_{n-j-1}] =0 for
all j, thereby reducing it to the known classification of simple linearly
compact Lie superalgebras and their Z-gradings. The list consists of four
examples, one of them being the n+1-dimensional vector product n-Lie algebra,
and the remaining three infinite-dimensional n-Lie algebras.Comment: Final version to appear in Communications in Mathematical Physic