Related papers: Tangential Star Products

Given a star product with separation of variables $\star$ on a pseudo-K\"ahler manifold $M$ and a point $x_0 \in M$, we construct an associative algebra of formal distributions supported at $x_0$. We use this algebra to express the formal…

Let ${\cal A}_1$ be the class of all unital separable simple $C^*$-algebras $A$ such that $A\otimes U$ has tracial rank at most one for all UHF-algebras of infinite type. It has been shown that amenable ${\cal Z}$-stable $C^*$-algebras in…

In this paper, several equivalent conditions on the Drazin invertibility of product and difference of idempotents are obtained in a ring. Some results in Banach algebra are extended to the ring case.

We prove a theorem about the derivation algebra of the tensor product of two algebras. As an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor…

Crossed product algebras are fundamental in the study of C*-algebras, traditionally under the assumption of continuity of group actions. Recent work by Grundling and Neeb introduced the crossed product host, an analog of the crossed product…

We provide a necessary and sufficient condition for separability of Gaussian states of bipartite systems of arbitrarily many modes. The condition provides an operational criterion since it can be checked by simple computation. Moreover, it…

A (vector space) basis B of a Lie algebra is said to be very nilpotent if all the iterated brackets of elements of B are nilpotent. In this note, we prove a refinement of Engel's Theorem. We show that a Lie algebra has a very nilpotent…

Let $F^\lambda_{\sigma} [G]$ be a crossed product of a group $G$ and the field $F$. We study the Lie properties of $F^\lambda_{\sigma} [G]$ in order to obtain a characterization of those crossed products which are upper (lower) Lie…

In this paper we introduce the notion of tangent space TG of a (not necessary smooth) subgroup G of the diffeomorphism group Diff(M) of a compact manifold M. We prove that TG is a Lie subalgebra of the Lie algebra of smooth vector fields on…

Let $X$ be a smooth projective curve of genus $g$ over an algebraically closed field $k$ of characteristic $p>2$. We prove that any rank $3$ nilpotent semistable Higgs bundle $(E,\theta)$ on $X$ is a strongly semistable Higgs bundle. This…

We present a classification of homogeneous star products on duals of Lie algebroids in terms of the second Lie algebroid cohomology. Moreover, we extend this classification to projectable star products, i.e., to quantizations compatible…

We give conditions under which a product of topological spaces satisfies some local property. The conditions are necessary and sufficient when the corresponding global property is preserved under finite products. Further examples include…

We study additively graceful labelings of signed graphs on stars and double stars. While the case of signed stars is straightforward, the problem becomes significantly more intricate for signed double stars. We obtain a characterization of…

Let X be a Banach space. Suppose that for all $p\in (1, \infty)$ a constant $C_{p,X}$ depending only on X and p exists such that for any two X-valued martingales f and g with tangent martingale difference sequences one has \[\E\|f\|^p \leq…

Let f be a differentiable function on the real line, and let P\inG_{f}^{C}= all points not on the graph of f. We say that the illumination index of P, denoted by I_{f}(P), is k if there are k distinct tangents to the graph of f which pass…

Let g be a simple simply laced Lie algebra. In this paper two families of varieties associated to the Dynkin graph of g are described: ``tensor product'' and ``multiplicity'' varieties. These varieties are closely related to Nakajima's…

We show that several known results about the algebraic K-theory of tensor products of algebras with the C*-algebra of compact operators in Hilbert space remain valid for tensor products with any properly infinite C*-algebra.

It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth, fiberwise-polynomial functions on the cotangent bundle a one-parameter family of graded star products. For a particular value…

Given a compact Lie group $G$ with Lie algebra $\mathfrak{g}$, we consider its tangent Lie group $TG\cong G\ltimes_{\mathrm{Ad}} \mathfrak{g}$. In this short note, we prove that $TG$ admits a left-invariant naturally reductive Riemannian…

Let (A,G,\alpha) be a partial dynamical system. We show that there is a bijective correspondence between G-invariant ideals of A and ideals in the partial crossed product A xr G provided the action is exact and residually topologically…