Related papers: DGLA Actions: An Application in GR
This thesis introduces the notion of "relative gerbes" for smooth maps of manifolds, and discusses their differential geometry. The equivalence classes of relative gerbes are classified by the relative integral cohomology in degree three.…
This thesis studies general relativity (GR) using chiral formulations, which take advantage of the decomposition of the four-dimensional Lorentz group into self-dual and anti-self-dual sectors. Within this framework, GR can be expressed…
We consider endomorphism actions of arbitrary discrete semigroups on a connected metrizable topological group G. We give necessary and sufficient conditions for expansiveness of such actions when G is a Lie group or a compact…
After reviewing some aspects of gravity in two dimensions, it is shown that non-trivial embeddings of sl(2) in a semi-simple (super) Lie algebra give rise to a very large class of extensions of 2D gravity. The induced action is constructed…
We classify group gradings on the simple Lie algebras of types $G_2$ and $D_4$ over the field of real numbers (or any real closed field): fine gradings up to equivalence and $G$-gradings, with a fixed group $G$, up to isomorphism.
A new method is introduced for doing calculations of quantum field theories in planar geometries which the metric depends on just one coordinate. In contrast to previous method, this method can be used in any planar geometry, not only…
Modified gravity theories have been suggested to address the limitations of general relativity, each exhibiting differences, particularly in their strong-field limits. Nonetheless, there lacks effective means to distinguish or test these…
We introduce a novel notion of {\it local spectral gap} for general, possibly infinite, measure preserving actions. We establish local spectral gap for the left translation action $\Gamma\curvearrowright G$, whenever $\Gamma$ is a dense…
The algebra and calculus of generalized differential forms are reviewed and employed to construct a class of generalized connections and to investigate their properties. The class includes generalized connections which are flat when…
The gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies: generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require…
Multisymplectic geometry is a generalization of symplectic geometry suitable for n-dimensional field theories, in which the nondegenerate 2-form of symplectic geometry is replaced by a nondegenerate (n+1)-form. The case n = 2 is relevant to…
Motivated by quantum-mechanical considerations we earlier suggested an alternative action for discretised quantum gravity which measures the perimeter of the space-time and has a dimension of length. It is the so called perimeter action,…
This paper is, essentially, a survey related to the problem of understanding the combinatorics of the action of the monoidal category of finite dimensional modules over a simple finite dimensional Lie algebra on various categories of Lie…
We show how one can do algebraic geometry with respect to the category of simplicial objects in an exact category. As a biproduct, we get a theory of derived analytic geometry.
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…
A section of a Riemannian $G$-manifold $M$ is a closed submanifold $\Sigma$ which meets each orbit orthogonally. It is shown that the algebra of $G$-invariant differential forms on $M$ which are horizontal in the sense that they kill every…
A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides…
In this work, we discuss the conditions that allow the establishment of an equivalence between $f(R,T)=R+\lambda h(T)$ gravity models and General Relativity (GR) coupled to a modified matter sector. We do so by considering a $D$-dimensional…
Recently, many researchers devoted their attention to study the extensions of the gamma and beta functions. In the present work, we focus on investigating some approximations for a class of Gauss hypergeometric functions by exploiting…
Algebraic geometry for groups and Lie algebraic has been recently defined and studied by many authors on the purpose to study set defined by algebraic equations on abstract groups and Lie algebras. The purpose of this paper is to present a…