Related papers: A Lie-algebraic approach to the local index theore…

Necessary and sufficient conditions for the exponentiation of finite-dimensional real Lie algebras of linear operators on complete Hausdorff locally convex spaces are obtained, focused on the equicontinuous case - in particular, necessary…

We consider a coamenable compact quantum group $\mathbb{G}$ as a compact quantum metric space if its function algebra $\mathrm{C}(\mathbb{G})$ is equipped with a Lip-norm. By using a projection $P$ onto direct summands of the Peter--Weyl…

The operator space analogue of the {\em strong form} of the principle of local reflexivity is shown to hold for any von Neumann algebra predual, and thus for any $C^{*}$-algebraic dual. This is in striking contrast to the situation for…

In this note, we use give some algebraic applications of a previous result by the author which compares the deformations parameterized by the Maurer-Cartan elements of a differential graded Lie algebra, and a differential graded Lie…

Let $M$ be a simply connected pseudo-Riemannian homogeneous space of finite volume with isometry group $G$. We show that $M$ is compact and that the solvable radical of $G$ is abelian and the Levi factor is a compact semisimple Lie group…

We consider the Dirac operator on asymptotically static Lorentzian manifolds with an odd-dimensional compact Cauchy surface. We prove that if Atiyah-Patodi-Singer boundary conditions are imposed at infinite times then the Dirac operator is…

In this paper, we prove Schwartz estimates for Hodge Laplacian and Dirac operators on semisimple Lie groups. Alongside, we gives a version of Kuga lemma for its Lie algebra cohomology. This is a generalization of similar results on…

We establish topological local rigidity for uniform lattices in compactly generated groups, extending the result of Weil from the realm of Lie groups. We generalize the classical local rigidity theorem of Selberg, Calabi and Weil to…

We prove a "quantified" version of the Weyl-von Neumann theorem, more precisely, we estimate the ranks of approximants to compact operators appearing in the Voiculescu's theorem applied to commutative algebras. This allows considerable…

First we give a new proof of Goto's theorem for Lie algebras of compact semisimple Lie groups using Coxeter transformations. Namely, every $x$ in $L = \operatorname{Lie}(G)$ can be written as $x =[a, b]$ for some $a$, $b$ in $L$. By using…

We give an infinitesimal criterion, in the analytic setting, for a vector space to be locally homogeneous under some group action. Our approach differs from those which resort to an inverse function theorem (e.g. those of Moser, Zehnder or…

A notion of local algebras is introduced in the theory of causal fermion systems. Their properties are studied in the example of the regularized Dirac sea vacuum in Minkowski space. The commutation relations are worked out, and the…

In this article we address the first part of the programme presented in \cite{Teleman_arXiv_III}, \S 2; we construct the local $K$- theory level of the index formula. Our construction is sufficiently general to encompass the algebra of…

After reviewing how the Borel-Weil-Bott theorem can be interpreted as an index theorem, we present a proof using Kostant's cubic Dirac operator and the equivariant McKean-Singer formula.

The purpose of this paper is to give a proof of the real part of the Riemann-Roch-Grothendieck theorem for complex flat vector bundles at the differential form level in the even dimensional fiber case. The proof is, roughly speaking, an…

We investigate the duality between algebraic and coalgebraic recognition of languages to derive a generalization of the local version of Eilenberg's theorem. This theorem states that the lattice of all boolean algebras of regular languages…

We introduce a new version $kk^{\rm alg}$ of bivariant $K$-theory that is defined on the category of all locally convex algebras. A motivating example is the Weyl algebra $W$, i.e. the algebra generated by two elements satisfying the…

Let $X$ be an affine algebraic variety with a transitive action of the algebraic automorphism group. Suppose that $X$ is equipped with several non-degenerate fixed point free $SL_2$-actions satisfying some mild additional assumption. Then…

We give a proof of the cobordism invariance of the index of elliptic pseudodifferential operators on sigma-compact manifolds, where, in the non-compact case, the operators are assumed to be multiplication outside a compact set. We show…

Given a proper, cocompact action of a Lie groupoid, we define a higher index pairing between invariant elliptic differential operators and smooth groupoid cohomology classes. We prove a cohomological index formula for this pairing by…