Related papers: Superconformal Vertex Algebras and Jacobi Forms
We investigate the Jacobian decomposition of some algebraic curves over finite fields with genus $4$, $5$ and $10$. As a corollary, explicit equations for curves that are either maximal or minimal over the finite field with $p^2$ elements…
Let $J(\pi)$ be the higher order Jacobi operator. We study algebraic curvature tensors where $J(\pi)J(\pi^{\perp})=J(\pi^{\perp})J(\pi)$. In the Riemannian setting, we give a complete characterization of such tensors; in the…
The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi…
We take first steps toward a theory of ``conformal twists'' for superconformal field theories in dimension 3 to 6, extending the well-known analysis of twists for supersymmetric theories. A conformal twist is a square-zero odd element in…
This is the 8th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. The article reviews the superconformal index. It is often simpler to calculate than instanton partition functions,…
Jacobi algebroids, that is graded Lie brackets on the Grassmann algebra associated with a vector bundle which satisfy a property similar to that of the Jacobi brackets, are introduced. They turn out to be equivalent to generalized Lie…
We show that the definition of a second order superintegrable system on a (pseudo-)Riemannian manifold gives rise to a conformally invariant notion of superintegrability. Conformal equivalence is the natural extension of the well-known…
In this paper, enveloping Lie superalgebras of Bol superalgebras are introduced. The notion of Killing-Ricci forms and invariant forms of these superalgebras are investigated as generalization of the ones of Bol algebras.
In this paper we study algebraic supergroups and their coadjoint orbits as affine algebraic supervarieties. We find an algebraic deformation quantization of them that can be related to the fuzzy spaces of non commutative geometry.
Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We…
This paper is devoted to the study of some connections between coadjoint orbits in infinite dimensional Lie algebras, isospectral deformations and linearization of dynamical systems. We explain how results from deformation theory,…
For a given Jacobi-Jordan algebra $A$ and a vector space $V$ over a field $k$, a non-abelian cohomological type object ${\mathcal H}^{2}_{A} \, (V, \, A)$ is constructed: it classifies all Jacobi-Jordan algebras containing $A$ as a…
We study quivers with relations given by non-commutative analogs of Jacobian ideals in the complete path algebra. This framework allows us to give a representation-theoretic interpretation of quiver mutations at arbitrary vertices. This…
The purpose of this paper is to introduce an algebraic cohomology theory of left pre-Jacobi-Jordan algebras. We use the cohomological approach to study linear deformations of these algebras. We also introduce the notion of Nijenhuis…
We discuss some properties of Jacobi fields that do not involve assumptions on the curvature endomorphism. We compare indices of different spaces of Jacobi fields and give some applications to Riemannian geometry.
We study the theta decomposition of Jacobi forms of nonintegral lattice index for a representation that arises in the theory of Weil representations associated to even lattices, and suggest possible applications.
In this note, we investigate Jacobian conjecture through investigation of automorphisms of polynomial rings in characteristic $p$. Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism…
We show that the Jacobi polynomials that are orthogonal on the unit circle (the Jacobi OPUC) are CMV bispectral. This means that the corresponding Laurent polynomials in the CMV basis satisfy two dual ordinary eigenvalue problems: a…
In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first…
In this paper, we introduce the representation theory of $\delta$-Hom-Jordan Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop the cohomology theory of Hom-Lie conformal superalgebras and…