Related papers: Curvature without connection
This is an expository paper in which we explain how basic, standard, results about simple Lie algebras can be obtained by geometric arguments, following ideas of Cartan, Richardson and others.
In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and…
Non-standard topics underlying a partly original approach to gauge field theory are concisely introduced, expressing ideas that were broached in several papers and, eventually, exposed in an organized form in a recently published book. By…
In this PhD thesis, we have studied certain geometric structures over Lie groupoids and differentiable stacks. This thesis is based on the work [arXiv:2103.04560, arXiv:2012.08447, arXiv:2012.08442, arXiv:1907.00375]. In [arXiv:1907.00375],…
In this paper we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group valued field with a prescribed gauge transformation. As an…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
In recent years, discrete spaces such as graphs attract much attention as models for physical spacetime or as models for testing the spirit of non-commutative geometry. In this work, we construct the differential algebras for graphs by…
We propose a general notion of algebraic gauge theory obtained via extracting the main properties of classical gauge theory. Building on a recent work on transferring curved $A_{\infty}$-structures we show that, under certain technical…
We develop the notions of connections and curvature for general Lie-Rinehart algebras without using smoothness assumptions on the base space. We present situations when a connection exists. E.g., this is the case when the underlying module…
We study the formal properties of correspondences of curves without a core, focusing on the case of \'{e}tale correspondences. The motivating examples come from Hecke correspondences of Shimura curves. Given a correspondence without a core,…
We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.
In this paper we introduce a new technique, based on dual quaternions, for the analysis of closed linkages with revolute joints: the theory of bonds. The bond structure comprises a lot of information on closed revolute chains with a…
In this paper an algebraic model for unbased rational homotopy theory from the perspective of curved Lie algebras is constructed. As part of this construction a model structure for the category of pseudo-compact curved Lie algebras with…
A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
We present a new approach for constructing covariant symplectic structures for geometrical theories, based on the concept of adjoint operators. Such geometric structures emerge by direct exterior derivation of underlying symplectic…
In the paper we prove, that extrinsic curvature does not impose restrictions on the topology of a contact structure, except the obvious ones.
A Lie algebra structure on variation vector fields along an immersed curve in a $2$-dimensional real space form is investigated. This Lie algebra particularized to plane curves is the cornerstone in order to define a Hamiltonian structure…
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…