Related papers: DGLA Actions: An Application in GR

We employ two-dimensional chiral algebra techniques to produce solutions of certain differential and integral equations which occur in the context of the Analytic Geometric Langlands Program.

Fundamentals on Lie group methods and applications to differential equations are surveyed. Many examples are included to elucidate their extensive applicability for analytically solving both ordinary and partial differential equations.

For actions with a dense orbit of a connected noncompact simple Lie group $G$, we obtain some global rigidity results when the actions preserve certain geometric structures. In particular, we prove that for a $G$-action to be equivalent to…

In this paper we introduce the notion of a 2-action of a Lie 2-algebra on an arbitrary manifold M. Furthermore, in [Rog12], given a n-plectic manifold (M, $\omega$), the authors consider a Lie Infinity-algebra L$\infty$ (M, $\omega$), which…

This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…

We introduce the notion of compatible actions in the context of split extensions of finite dimensional Lie algebras over a field. Using compatible actions, we construct a new resolution to compute the cohomology of semi-direct products of…

In the standard orbit model on shape analysis, a group of diffeomorphism on the ambient space equipped with a right invariant sub-riemannian metric acts on a space of shapes and induces a sub-riemannian structure on various spaces. An…

We consider the domain of applicability of general relativity (GR), as a classical theory of gravity, by considering its applications to a variety of settings of physical interest as well as its relationship with real observations. We argue…

One of the central concepts in modern theoretical physics, gauge symmetry, is typically realised by lifting a finite-dimensional global symmetry group of a given functional to an infinite-dimensional local one by extending the functional to…

We present affine Lie algebras generated by the supercovariant derivatives and the supersymmetry generators for the left and right moving modes in the doubled space. Chirality is manifest in our doubled space as well as the T-duality…

General Relativity (GR) exists in different formulations. They are equivalent in pure gravity but generically lead to distinct predictions once matter is included. After a brief overview of various versions of GR, we focus on metric-affine…

We study the spectral action approach to higher derivative gravity. The work focuses on the classical aspects. We derive the complete and simplified form of the purely gravitational action up to the 6-derivative terms. We also derive the…

For a manifold M we define a structure on the group action of Diff(M) on the smooth functions on M which reduces to the usual differential geometry upon differentiation at zero along the one-parameter groups of Diff(M). This ``integrated…

We present a mathematical framework of gauge theories that is based upon a skew-adjoint Lie algebra and a generalized Dirac operator, both acting on a Hilbert space.

We give explicit formulae for a differential graded Lie algebra (DGLA) model of the triangle which is symmetric under the geometric symmetries of the cell. This follows the work of Lawrence-Sullivan on the (unique) DGLA model of the…

This paper does not contain any new results, it is just an attempt to present, in a systematic way, one construction which establishes an interesting relationship between some ideas and notions well-known in the theory of integrable systems…

Starting from the original Einstein action, sometimes called the Gamma squared action, we propose a new setup to formulate modified theories of gravity. This can yield a theory with second order field equations similar to those found in…

We present the most general actions of a single scalar field and two scalar fields coupled to gravity, consistent with second order field equations in four dimensions, possessing local scale invariance. We apply two different methods to…

We discuss the differential graded Lie algebra (DGLA) of Drinfeld modeled on the tensor algebra of the universal enveloping algebra of a Lie algebra g over any field K of characteristic zero. We explicitly analyze the first obstruction to…

This paper presents a survey of the results and ideas behind the classification of the fine gradings, up to equivalence, on the simple finite dimensional Lie algebras over an algebraically closed field of characteristic zero. It provides an…