A simple axiomatic characterization of the noncommutative Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. It is proved that every quotient Itô algebra has a faithful representation in a Minkowski space and is canonically decomposed into the orthogonal sum of quantum Brownian (Wiener) algebra and quantum Lévy (Poisson) algebra. In particular,...

This article is a further contribution to our research [1] into a class of infinite-dimensional Lie algebras L∞(N+, N−) generalizing the standard W∞ algebra, viewed as a tensor operator algebra of SU(1, 1) in a group-theoretic framework. Here we interpret L∞(N+, N−) either as a infinite continuation of pseudo-unitary symmetries U(N+, N−), or as a “higher-U(N+, N−)-spin extension” of the diffeom...

We survey a recent extension of the moving frames method for infinite-dimensional Lie pseudo-groups. Applications include a new, direct approach to the construction of Maurer–Cartan forms and their structure equations for pseudogroups, and new algorithms, based on constructive commutative algebra, for uncovering the structure of the algebra of differential invariants for pseudogroup actions.

We consider the pair (pi, fi) as a force with two-dimensional direction vector fi applied at the point pi in the plane. For a given set of forces we ask for a non-crossing geometric graph on the points pi that has the following property: There exists a weight assignment to the edges of the graph, such that for every pi the sum of the weighted edges (seen as vectors) around pi yields −fi. As add...

Abstract We establish the dual equivalence of category generalized (i.e., potentially nonunital) operator systems and pointed compact noncommutative (nc) convex sets, extending a result Davidson 1st author. then apply this to number results about systems, some which are new even in unital setting. For example, we show that maximal minimal C*-covers system can be realized terms theC*-algebra con...

In this paper we consider the flip operation for combinatorial pointed pseudo-triangulations where faces have size 3 or 4, so-called combinatorial 4-PPTs. We show that every combinatorial 4-PPT is stretchable to a geometric pseudo-triangulation, which in general is not the case if faces may have size larger than 4. Moreover, we prove that the flip graph of combinatorial 4-PPTs is connected and ...

It is pointed out that the usual θ-algebra assumed for non-commuting coordinates is not P and T -invariant, unless one formally transforms the non-commutativity parameter θ in an appropriate way. On the other hand, the Lorentz-covariant DFR algebra, which ‘relativitizes’ the θ-algebra by replacing θ with a second-rank antisymmetric tensor operator θ̂ , is P and T -invariant. It is then proved th...

Recall that a commutative ring R is said to be a pseudo-valuation ring if every prime ideal of R is strongly prime. We define a completely pseudovaluation ring. Let R be a ring (not necessarily commutative). We say that R is a completely pseudo-valuation ring if every prime ideal of R is completely prime. With this we prove that if R is a commutative Noetherian ring, which is also an algebra ov...

We show that O(n) exchanging flips suffice to transform any edge-labelled pointed pseudo-triangulation into any other with the same set of labels. By using insertion, deletion and exchanging flips, we can transform any edge-labelled pseudo-triangulation into any other with O(n log c+h log h) flips, where c is the number of convex layers and h is the number of points on the convex hull.