Related papers: More Abelian Dualities in 2+1 Dimensions
We develop a technique that solders the dual aspects of some symmetry following from the bosonisation of two distinct fermionic models, thereby leading to new results which cannot be otherwise obtained. Exploiting this technique, the two…
In this paper we generalize previous work on decomposition in three-dimensional orbifolds by 2-groups realized as analogues of central extensions, to orbifolds by more general 2-groups. We describe the computation of such orbifolds in…
We apply the method of differential renormalization to two and three dimensional abelian gauge theories. The method is especially well suited for these theories as the problems of defining the antisymmetric tensor are avoided and the…
We propose a new class of infrared dualities relating three-dimensional $\mathcal{N}=2$ $USp(2N)$ Chern--Simons SQCD to planar Abelian quiver gauge theories. These dual descriptions are constructed via real mass deformations of established…
We count the number of isomorphism classes of degree $d$-twists of some polarized abelian varieties over finite fields of odd prime dimension. This can be seen as a higher dimensional analogue of the counting problem for elliptic curves…
Let k be an algebraically closed field of odd characteristic. We describe derivations of a large class of quantizations of affine normal Poisson varieties over k.
This paper addresses the classification problem of associative algebras over arbitrary base fields. We present a list of three-dimensional associative algebras with canonical representatives of the isomorphism classes for fields of…
We study restricted homomorphism dualities in the context of classes with bounded expansion. This presents a generalization of restricted dualities obtained earlier for bounded degree graphs and also for proper minor closed classes. This is…
In the paper we give a complete classification of $2$-dimensional evolution algebras over algebraically closed fields, describe their groups of automorphisms and derivation algebras.
We provide a coarse classification of all 8-dimensional Manin triples, that describe Poisson--Lie T-dualities between 4-dimensional group manifold solutions to supergravity equations. We find several such dualities and one Poisson--Lie…
We initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization of derivations has an analogue in the theory of associative…
In this work we present some arithmetic properties of families of abelian $p$--extensions of global function fields, among which are their generators and their type of ramification and decomposition.
A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the second-order Abel equation and the existence of two alternative…
We discuss a recent line of research investigating inverse theorems with respect to general k-wise correlations, and explain how such correlations arise in different contexts in mathematics. We outline some of the results that were…
The algebraic and geometric classification of all complex $3$-dimensional transposed Poisson algebras is obtained. Also, we discuss strong special $3$-dimensional transposed Poisson algebras.
The aim of this paper is to introduce the theory of Abelian integrals for holomorphic foliations in a complex manifold of dimension two. We will show the importance of Picard-Lefschetz theory and the classification of relatively exact…
We give a brief survey of abelian torsions of 3-manifolds.
Starting with the N=8 supersymmetric Yang-Mills theory on D2-branes and incorporating higher-derivative corrections to lowest nontrivial order, we perform a duality to derive the Lorentzian 3-algebra theory along with a set of derivative…
We prove the modularity of a positive proportion of abelian surfaces over $\mathbf{Q}$. More precisely, we prove the modularity of abelian surfaces which are ordinary at $3$ and are $3$-distinguished, subject to some assumptions on the…
We bosonise the complex-boson realisations of the $W_\infty$ and $W_{1+\infty}$ algebras. We obtain nonlinear realisations of $W_\infty$ and $W_{1+\infty}$ in terms of a pair of fermions and a real scalar. By further bosonising the…