Related papers: Strict Almost Non-Abelian Deformations
After a brief survey of the appearance of quantum algebras in diverse contexts of quantum gravity, we demonstrate that the particular deformed algebras, which arise within the approach of J.Nelson and T.Regge to 2+1 anti-de Sitter quantum…
The purpose of this paper is to present the extended definitions and characterizations of the classical notions of APN and maximum nonlinear Boolean functions to deal with the case of mappings from a finite group K to another one N with the…
We analyze a recent conjecture regarding the perturbative construction of non-linear deformations of all classically duality invariant theories, including N=8 supergravity. Starting with an initial quartic deformation, we engineer a…
If $a$ is a densely defined sectorial form in a Hilbert space which is possibly not closable, then we associate in a natural way a holomorphic semigroup generator with $a$. This allows us to remove in several theorems of semigroup theory…
The article is devoted to the investigation of properties of quasi-invariant measures with values in non-Archimedean fields such as: convolutions of measures and functions; continuity of functions of measures; non-associative noncommutative…
The unitary implementation of a symmetry group $G$ of a classical system in the corresponding quantum theory entails unavoidable deformations $\TG$ of $G$, namely, central extensions by the typical phase invariance group U(1). The…
We show that the Born-Infeld theory with n complex abelian gauge fields written in an auxiliary field formulation has a U(n,n) duality group. We conjecture the form of the Lagrangian obtained by eliminating the auxiliary fields and then…
We show that a complex structure on a nilpotent almost abelian real Lie algebra is unique if it exists. As a consequence, we get full control over the cohomology and deformations of almost abelian complex nilmanifolds.
We study in more detail the cubic constraints for N=1 chiral superfields proposed in the earlier work Eur. Phys. J. C 81, 523 (2021), which describe low-energy goldstino-axion dynamics in global non-linearly realized supersymmetry. We…
For every natural number k we introduce the notion of k-th order convolution of functions on abelian groups. We study the group of convolution preserving automorphisms of function algebras in the limit. It turns out that such groups have…
Any deformation of a Weyl or Clifford algebra can be realized through some change of generators in the undeformed algebra. Here we briefly describe and motivate our systematic procedure for constructing all such changes of generators for…
Deformations of the Lie algebras so(4), so(3,1), and e(3) that leave their so(3) subalgebra undeformed and preserve their coset structure are considered. It is shown that such deformed algebras are associative for any choice of the…
In N=2 supersymmetric QCD with the U(N) gauge group and N_f>N we study the crossover transition from the weak coupling regime at large \xi to strong coupling at small \xi where \xi is the Fayet--Iliopoulos parameter. We find that at strong…
We study the action of non-Abelian T-duality in the context of N=1 geometries with well understood field theory duals. In the conformal case this gives rise to a new solution that contains an AdS_5 X S^2 piece. In the case of non-conformal…
Motivated by application to multiple M5 branes, we study some properties of non-Abelian two-form gauge theories. We note that the fake curvature condition which is commonly used in the literature would restrict the dynamics to be either a…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
We define the notion of adjustment for strict Lie 2-groups and provide the complete cocycle description for non-Abelian gerbes with connections whose structure 2-group is an adjusted 2-group. Most importantly, we depart from the common…
In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the well-known deformation theory of algebras developed by Gerstenhaber. As part of our deformation…
We use the theory of the quantum group $U_q(gl(2,\RR))$ in order to develop a quantum theory of invariants and show a decomposition of invariants into a Gordan-Capelli series. Higher binary forms are introduced on the basis of braided…
This is an addendum to the paper ``Deformation of $L_\infty$-Algebras'' of the same author. We explain in which way the deformation theory of $L_\infty$-algebras extends the deformation theory of singularities. We show that the construction…