Related papers: Free actions and Grassmanian variety

We prove that the classical algebraic varieties over algebraically closed fields can be defined over arbitrary fields $k.$ Then we prove that for associative algebras $A$, there exist local representing objects $A_M$ for simple modules $M.$…

Let $X$ be an algebraic variety equipped with a dominant rational self-map $\phi:X\to X$. A new quantity measuring the interaction of $(X,\phi)$ with trivial dynamical systems is introduced; the stabilised algebraic dimension of $(X,\phi)$…

General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or…

For a simple linear algebraic group $G$ acting faithfully on a vector space $V$ and under mild assumptions, we show: if $V$ is large enough, then the Lie algebra of $G$ acts generically freely on $V$. That is, the stabilizer in the Lie…

We prove that measure-class-preserving non-amenable treeable equivalence relations of type III, meaning not preserving any equivalent $\sigma$-finite measure, are induced by free actions of non-abelian free groups of any given number of…

In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this…

Define an arithmetic variety to be the quotient of a bounded symmetric domain by an arithmetic group. An arithmetic variety is algebraic, and the theorem in question states that when one applies an automorphism of the field of complex…

We associate with the Grassmann algebra a topological algebra of distributions, which allows the study of processes analogous to the corresponding free stochastic processes with stationary increments, as well as their derivatives.

We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…

We reformulate Einstein's theory of gravity, isolating the conformal degree of freedom in a covariant way. This is done by introducing a physical metric defined in terms of an auxiliary metric and a scalar field appearing through its first…

We study the $t$-deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if $t$ sufficiently…

We prove a decomposition theorem for the equivariant K-theory of actions of affine group schemes G of finite type over a field on regular separated noetherian algebraic spaces, under the hypothesis that the actions have finite geometric…

Let I be a finite set and CI be the algebra of functions on I. For a finite dimensional C algebra A with \CI contained in A we show that certain moduli spaces of finite dimsional modules are isomorphic to certain Grassmannian (quot-type)…

We describe some of the connections between the Bieri-Neumann-Strebel-Renz invariants, the Dwyer-Fried invariants, and the cohomology support loci of a space X. Under suitable hypotheses, the geometric and homological finiteness properties…

We define the notion of action of an L-infinity algebra $g$ on a graded manifold $M$, and show that such an action corresponds to a homological vector field on $g[1] \times M$ of a specific form. This generalizes the correspondence between…

A variety is a class of algebraic structures axiomatized by a set of equations. An equation is linear if there is at most one occurrence of an operation symbol on each side. We show that a variety axiomatized by linear equations has the…

We exhibit a simple and explicit formula for the metric of an arbitrary static spherically symmetric perfect fluid spacetime. This class of metrics depends on one freely specifiable monotone non-increasing generating function. We also…

The first part of this paper is a refinement of Winkelmann's work on invariant rings and quotients of algebraic groups actions on affine varieties, where we take a more geometric point of view. We show that the (algebraic) quotient…

A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…

We define a GL-variety to be a (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms a polynomial representation. Such varieties have been used…