相关论文: Degenerate Spin Structures and the Levy-Leblond Eq…

The consistent, local, smooth deformations of the dual formulation of linearized gravity involving a tensor field in the exotic representation of the Lorentz group with Young symmetry type (D-3,1) (one column of length D-3 and one column of…

The Lagrange--Poincar\'e equations for the mechanical system describing the motion of a scalar particle on a Riemannian manifold with a given free and isometric action of a compact Lie group is obtained. In an arising principle fibre…

An integrated approach to Lie derivatives of spinors, spinor connections and the gravitational field is presented, in the context of a previously proposed, partly original formulation of a theory of Einstein-Carta-Maxwell-Dirac fields based…

Division algebras have demonstrated their utility in studying non-associative algebras and their connection to the Standard Model through complex Clifford algebras. This article focuses on exploring the connection between these complex…

On a Riemannian or a semi-Riemannian manifold, the metric determines invariants like the Levi-Civita connection and the Riemann curvature. If the metric becomes degenerate (as in singular semi-Riemannian geometry), these constructions no…

New Galilei quantum groups dual to the Hopf algebras proposed in [1] are obtained by the nonrelativistic contraction procedures. The corresponding Lie-algebraic and quadratic quantum space-times are identified with the translation sectors…

We give a formula for the spectral pairs (after Steenbrink) for composite singularities of several variables. (Note that for two variable case is studyed by Nemethi-Steenbrink.) Here composite singularity is given by the equation f(g_1,…

Degeneracy loci of morphisms between vector bundles have been used in a wide variety of situations. We introduce a vast generalization of this notion, based on orbit closures of algebraic groups in their linear representations. A preferred…

We study the non-relativistic Newton-Cartan limit of higher-order gravity theories in arbitrary dimensions. We first study it at the level of the action by introducing an additional 1-form gauge field and coupling it appropriately to the…

We consider a family of Levi-degenerate finite type hypersurfaces in $\mathbb C^2$, where in general there is no group structure. We lift these domains to stratified Lie groups via a constructive proof, which optimizes the well-known…

Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of reducible degenerate Lagrangian systems,…

In this paper we define a Dirichlet-to-Neumann map for a twisted Dirac Laplacian acting on bundle-valued spinors over a spin manifold. We show that this map is a pseudodifferential operator of order 1 whose symbol determines the Taylor…

Cubic couplings between a complex scalar field and a tower of symmetric tensor gauge fields of all ranks are investigated. A symmetric conserved current, bilinear in the scalar field and containing r derivatives, is provided for any rank…

Studied are moduli spaces of self dual or anti-self dual connections on noncommutative 4-manifolds, especially deformation quantization of compact spin Riemannian 4-manifolds and their isometry groups have 2-torus subgroup. Then such moduli…

A *-product compatible with the comultiplication of the Hopf algebra of the functions on the Heisenberg group is determined by deforming a coboundary Lie-Poisson structure defined by a classical r-matrix satisfying the modified Yang-Baxter…

The Dijkgraaf-Vafa approach is used in order to study the Coulomb branch of the Leigh-Strassler massive deformation of N=4 SYM with gauge group U(N). The theory has N=1 SUSY and an N-dimensional Coulomb branch of vacua, which can be…

We provide a formal definition of p-brane Newton--Cartan (pNC) geometry and establish some foundational results. Our approach is the same followed in the literature for foundations of Newton--Cartan Gravity. Our results provide control of…

In this paper we show that Cartan geometries can be studied via transitive Lie groupoids endowed with a special kind of vector-valued multiplicative 1-forms. This viewpoint leads us to a more general notion, that of Cartan bundle, which…

We study properties of Newton-Cartan gravity under transformations into all noninertial, nonrelativistic reference frames. The set of these transformations has the structure of an infinite dimensional Lie group, called the Galilean line…

We compute the mapping class group-valued monodromy of any sufficiently ample linear system on any smooth simply connected projective surface, identifying this with the r-spin mapping class group associated to a maximal root of the adjoint…