Related papers: Einstein Algebras in a Categorical Context
Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to general relativity. The corresponding…
A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous Einstein space) is almost completely determined by the nilradical of its Lie algebra. A nilpotent Lie algebra, which can serve as the nilradical of an Einstein metric…
We present a common framework to study varieties in great generality from a categorical point of view. The main application of this study is in the setting of algebraic categories, where we introduce Birkhoff varieties which are essentially…
We deal with stability theory for ``reasonable'' non-elementary classes without any remanents of compactness (like: above Hanf number or definable by L_{omega_1, omega}).
In this note, we show that a nontrivial, compact, degenerate or nondegenerate, gradient Einstein-type manifold of constant scalar curvature is isometric to the standard sphere with a well defined potential function. Moreover, under some…
We introduce a new class of finite dimensional gentle algebras, the surface algebras, which are constructed from an unpunctured Riemann surface with boundary and marked points by introducing cuts in internal triangles of an arbitrary…
The possibility of the extension of spatial diffeomorphisms to a larger family of symmetries in a class of classical field theories is studied. The generator of the additional local symmetry contains a quadratic kinetic term and a potential…
Assuming the von Neumann algebra associated with a generic de Sitter observer is properly infinite (type III) we use Connes cocycle to identify the unique ( up to unitary equivalence) background independent dominant weight on an extended…
A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the…
We study general nilpotent algebras. The results obtained are new even for the classical algebras, such as associative or Lie algebras. We single out certain generic properties of finite-dimensional algebras, mostly over infinite fields.…
If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime.…
An Einstein nilradical is a nilpotent Lie algebra, which can be the nilradical of a metric Einstein solvable Lie algebra. The classification of Riemannian Einstein solvmanifolds (possibly, of all noncompact homogeneous Einstein spaces) can…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
Algebraic theories, sometimes called equational theories, are syntactic notions given by finitary operations and equations, such as monoids, groups, and rings. There is a well-known category-theoretic treatment of them that algebraic…
Universal algebraic geometry allows considering of geometric properties of every universal algebra. When two algebras have same algebraic geometry? We must consider the categories of algebraic closed sets of these algebras to answer this…
The black hole area theorem suggests that classical general relativity is the thermodynamic limit of a quantum statistics. The degrees of freedom of the statistical theory cannot be the spacetime metric. We argue that the statistical theory…
The topos theory is a theory which is used for deciding a number of problems of theory of relativity, gravitation and quantum physics. In the article spherically symmetric solution of the vacuum Einstein equations in the Intuitionistic…
Einstein's General Relativity (GR) is a dynamical theory of the spacetime metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearised level and show how a gauge theoretic Lagrangian for…
Our purpose here is to introduce the idea of viewing the spacetime as a macroscopic complex system which, consequently, cannot be directly quantized. It should be thought of as a collection of more fundamental "microscopical" entities…
The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of…