Related papers: On dual definite subspaces in Krein space
Dynkin's classification of maximal subalgebras of simple finite dimensional complex Lie algebras is generalized to Lie subsuperalgebras of the general linear Lie superalgebras.
In this paper, we consider hypergraphs whose vertices are distinct points moving smoothly on a Riemannian manifold M. We take these hypergraphs as graded submanifolds of configuration spaces. We construct double complexes of differential…
We discuss "Banach SN spaces", which include Hilbert spaces, negative Hilbert spaces, and the product of any real Banach space with its dual. We introduce "L-positive" sets, which generalize monotone multifunctions from a Banach space into…
We give a broad overview of superstring duality, Dirichlet branes, and some implications of both for questions about the structure of space-time at short distances.
In this review, we give a pedagogical introduction to a systematic framework for constructing and analyzing supersymmetric field theories on curved spacetime manifolds. The framework is based on the use of off-shell supergravity background…
We give an overview of D-branes in the maximally supersymmetric plane wave background of IIB supergravity. We start by reviewing the results of the probe analysis. We then present the open string analysis and show how certain spacetime…
Higher dimensional supersymmetric quantum mechanics is studied. General properties of the two dimensional case are presented. For three spatial dimesions or higher, a spin structure is shown to arise naturally from the nonrelativistic…
We discuss supernear spaces.
We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C^n. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries…
We introduce a class of metrics on $\mathbb{R}^n$ generalizing the classical Grushin plane. These are length metrics defined by the line element $ds = d_E(\cdot,Y)^{-\beta}ds_E$ for a closed nonempty subset $Y \subset \mathbb{R}^n$ and…
Duality symmetries in supergravity theories, together with their implications for string theory, are reviewed.
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
We find a one-to-one correspondence between full extrinsic symmetric spaces in (possibly degenerate) inner product spaces and certain algebraic objects called (weak) extrinsic symmetric triples. In particular, this yields a description of…
We consider biharmonic submanifolds in both generalized complex and Sasakian space forms. After giving the biharmonicity conditions for submanifolds in these spaces, we study different particular cases for which we obtain curvature…
In the first part of this expository article, the most important constructions and classification results concerning totally geodesic submanifolds in Riemannian symmetric spaces are summarized. In the second part, I describe the results of…
Many two-dimensional classical field theories have hidden symmetries that form an infinite-dimensional algebra. For those examples that correspond to effective descriptions of compactified superstring theories, the duality group is expected…
We define the corresponding Hardy space, Schur multipliers and their realizations, and interpolation. Possible applications of the present work include matrices of quaternions, matrices of split quaternions, and other algebras of…
In this paper we provide a study of quaternionic inner product spaces. This includes ortho-complemented subspaces, fundamental decompositions as well as a number of results of topological nature. Our main purpose is to show that a uniformly…
After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.
Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy are characterized by symmetries related to covariantly constant forms that these manifolds hold, which are generally non-linear and close in a…