Related papers: Model Theory of Generic Vector Space Endomorphisms

A certain vector-tensor (VT) theory is revisited. It was proposed and analyzed as a theory of electromagnetism without the standard gauge invariance. Our attention is first focused on a detailed variational formulation of the theory, which…

We compare the invariants of flat vector bundles defined by Atiyah et al. and Jones et al. and prove that, up to weak homotopy, they induce the same map, denoted by $e$, from the $0$-connective algebraic $K$-theory space of the complex…

A vector space is commonly defined as a set that satisfies several conditions related to addition and scalar multiplication. However, for beginners, it may be hard to immediately grasp the essence of these conditions. There are probably a…

For any finite dimensional C^*-algebra A with a trace vector \vec s whose entries are rational numbers, we give an endomorphism \Phi of the hyperfinite II_1 factor R such that: for all k \in \mathbb {N}, \Phi^k (R)' \cap R= \otimes^k A. The…

The Kalman variety of a linear subspace in a vector space consists of all endomorphism that possess an eigenvector in that subspace. We study the defining polynomials and basic geometric invariants of the Kalman variety.

A linear mapping upon real n-dimensional space, where the dimension n is odd, has a real eigenvalue-eigenvector pair. The corresponding statement for complex vector spaces holds true for any dimension n, but should be easy to demonstrate…

The goal of this paper is to generalize the theory of triangularizing matrices to linear transformations of an arbitrary vector space, without placing any restrictions on the dimension of the space or on the base field. We define a…

A subspace $X$ of a vector space over a field $K$ is hyperinvariant with respect to an endomorphism $f$ of $V$ if it is invariant for all endomorphisms of $V$ that commute with $f$. We assume that $f$ is locally nilpotent, that is, every $…

Let V be a smooth variety defined over the real numbers. Every algebraic vector bundle on V induces a complex vector bundle on the underlying topological space V(C), and the involution coming from complex conjugation makes it a Real vector…

Correspondences between k-tuples of points are key in multiple view geometry and motion analysis. Regular transformations are posed by homographies between two projective planes that serves as structural models for images. Such…

Consider the expansion $T_S$ of a theory $T$ by a predicate for a submodel of a reduct $T_0$ of $T$. We present a setup in which this expansion admits a model companion $TS$. We show that the nice features of the theory $T$ transfer to…

We prove a generalization of the fundamental theorem of algebraic K-theory for Verdier-localizing functors by extending the proof for algebraic K-theory of spaces to the realm of stable $\infty$-categories. The formula behaves much better…

A first-order theory $T$ is a model-complete core theory if every first-order formula is equivalent modulo $T$ to an existential positive formula; the core companion of a theory $T$ is a model-complete core theory $S$ such that every model…

Let F_n be the fixed-point algebra of the gauge action of the circle on the Cuntz algebra O_n. For every pure state \rho of F_n and every representation \theta of C(T) we construct a representation of O_n, and we use the resulting class of…

The two main theorems proved here are as follows: If $A$ is a finite dimensional algebra over an algebraically closed field, the identity component of the algebraic group of outer automorphisms of $A$ is invariant under derived equivalence.…

Let $B$ be a simply-connected projective variety such that the first cohomology groups of all line bundles on $B$ are zero. Let $E$ be a vector bundle over $B$ and $X={\mathbb P} (E)$. It is easily seen that a power of any endomorphism of…

We offer here a more direct approach to twisted K-theory, based on the notion of twisted vector bundles (of finite or infinite dimension) and of twisted principal bundles. This is closeely related to the classical notion ot torsors and…

Kikyo and Shelah showed that if $T$ is a theory with the Strict Order Property in some first-order language $\mathcal{L}$, then in the expanded language $\mathcal{L}_\sigma := \mathcal{L}\cup\{\sigma\}$ with a new unary function symbol…

With any (open or closed) cover of a space T we associate certain homotopy classes of maps T into n-spheres. These homotopy invariants can be considered as obstructions for extensions of covers of a subspace A to a space X. We using these…

Starting from an arbitrary endomorphism $\alpha$ of a unital C*-algebra $A$ we construct a bigger C*-algebra $B$ and extend $\alpha$ onto $B$ in such a way that the extended endomorphism $\alpha$ has a unital kernel and a hereditary range,…