Related papers: BMS-like algebras: canonical realisations and BRST…
In this paper, we find a class of Carrollian and Galilean contractions of (extended) BMS algebra in 3+1 and 2+1 dimensions. To this end, we investigate possible embeddings of 3D/4D Poincar\'{e} into the BMS${}_3$ and BMS${}_4$ algebras,…
We discuss the cosmological evolution of the Weyl conformal geometry and its associated Weyl quadratic gravity. The Einstein gravity (with a positive cosmological constant) is recovered in the spontaneously broken phase of Weyl gravity;…
We consider the extension of the general-linear and special-linear algebras by employing the Maxwell symmetry in $D$ space-time dimensions. We show how various Maxwell extensions of the ordinary space-time algebras can be obtained by a…
Corresponding to the Bondi-Metzner-Sachs (BMS) symmetry algebra of asymptotically-flat spacetimes are a set of BMS charges. These are formally constructed via the symplectic formalism of Wald and Zoupas, but the same charge expression may…
The BRST-anti-BRST covariant extension is suggested for the split involution quantization scheme for the second class constrained theories. The constraint algebra generating equations involve on equal footing a pair of BRST charges for…
Starting from a Lie algebroid ${\cal A}$ over a space V we lift its action to the canonical transformations on the principle affine bundle ${\cal R}$ over the cotangent bundle $T^*V$. Such lifts are classified by the first cohomology…
Quantum Lie algebras (an important class of quadratic algebras arising in the Woronowicz calculus on quantum groups) are generalizations of Lie (super) algebras. Many notions from the theory of Lie (super)algebras admit ``quantum''…
We investigate the quantum structure of spacetime at fundamental scales via a novel, Lorentz-invariant noncommutative coordinate framework. Building on insights from noncommutative geometry, spectral theory, and algebraic quantum field…
The first part of this thesis focuses on the Weyl-covariant nature of holography. We generalize the Fefferman-Graham ambient construction for conformal geometry to a corresponding construction for Weyl geometry. Through the Weyl-ambient…
A new approach for obtaining the three-dimensional Chern-Simons supergravity for the Poincar\'e algebra is presented. The $\mathcal{N}$-extended Poincar\'e supergravity is obtained by expanding the super Lorentz theory. We extend our…
The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's…
We present an algebraic classification, based on the null alignment properties of the Weyl tensor, of the general Kundt class of spacetimes in arbitrary dimension for which the non-expanding, non-twisting, shear-free null direction \boldk…
We study all the symmetries of the free Schr\"odinger equation in the non-commutative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated…
A notion of quantum matrix (QM-) algebra generalizes and unifies two famous families of algebras from the theory of quantum groups: the RTT-algebras and the reflection equation (RE-) algebras. These algebras being generated by the…
The asymptotic structure of three-dimensional hypergravity without cosmological constant is analyzed. In the case of gravity minimally coupled to a spin-$5/2$ field, a consistent set of boundary conditions is proposed, being wide enough so…
The article concerns the subalgebra U_v^+(w) of the quantized universal enveloping algebra of the complex Lie algebra sl_{n+1} associated with a particular Weyl group element of length 2n. We verify that U_v^+(w) can be endowed with the…
We perform a complete and systematic analysis of the solution space of six-dimensional Einstein gravity. We show that a particular subclass of solutions -- those that are analytic near $\mathcal{I}^+$ -- admit a non-trivial action of the…
We show that a class of solutions of minimal supergravity in five dimensions is given by lifts of three--dimensional Einstein--Weyl structures of hyper-CR type. We characterise this class as most general near--horizon limits of…
In this paper we pursue further a programme initiated in a previous work and aimed at the construction, classification and property investigation of time dependent solutions of supergravity (superstring backgrounds) through a systematic…
Pure $R^2$ gravity was considered originally to possess only global scale symmetry. It was later shown to have the larger restricted Weyl symmetry where it is invariant under the Weyl transformation $g_{\mu\nu} \to \Omega^2(x)\, g_{\mu\nu}$…