Related papers: Classification of outer actions of Z^N on O_2

It is shown that certain quasi-free flows on the Cuntz algebra $O_\infty$ have the Rohlin property and therefore are cocycle-conjugate with each other. This, in particular, shows that any unital separable nuclear purely infinite simple…

We study groups of C^1 orientation-preserving homeomorphisms of the plane, and pursue analogies between such groups and circularly-orderable groups. We show that every such group with a bounded orbit is circularly-orderable, and show that…

The co-Lie structures compatible with the osp(2|2) Lie super algebra structure are investigated and found to be all of coboundary type. The corresponding classical r-matrices are classified into several disjoint families. The osp(1|2)+u(1)…

We show that the $N=2$ and $N=4$ SUSY Yang-Mills action can be reformulated in the sense of non-commutative geometry on $M^4\times (Z_2\oplus Z_2)$ in a rather simple way. In this way the scalars or pseudoscalars are viewed as gauge fields…

In this paper we define a $\mathbf{QP}^1$-valued class function on the mapping class group $\mathcal{M}_{g,2}$ of a surface $\Sigma_{g,2}$ of genus $g$ with two boundary components. Let $E$ be a $\Sigma_{g,2}$ bundle over a pair of pants…

We explain a Macaulay2 implementation of a construction, which appeared in [Holweck-Oeding arXiv:2206.13662], of a graded algebra structure on the direct sum of a Lie algebra $\mathfrak{g}$ (typically $\mathfrak{sl}_n$) and a…

Let $G$ be a group acting freely, properly discontinuously and cellularly on a finite dimensional $C$W-complex $\Sigma(2n)$ which has the homotopy type of the $2n$- sphere $\mathbb{S}^{2n}$. Then, this action induces an action of the group…

A superparticle action which is globally supersymmetric in the target space is proposed. The supersymmetry is the supersymmetric extension of the rotation group O(3).

We classify exterior fibrations in the exterior homotopy category. As a result we also classify proper fibrations between CW-complexes.

We consider the conjugation action of a quantum group over an arbitrary field. In particular we consider the coordinate algebra of a quantised general linear group G(n), at an arbitrary nonzero parameter q, and give analogues of results of…

We prove that even Coxeter groups, whose Coxeter diagrams contain no (4,4,2) triangles, are conjugacy separable. In particular, this applies to all right-angled Coxeter groups or word hyperbolic even Coxeter groups. For an arbitrary Coxeter…

The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite groups. We also compare the classical, exterior and symmetric…

Let K be a an alternating prime knot in the 3-sphere. We investigate the category of flypes between reduced alternating diagrams for K. As a consequence, we show that any odd prime order action on K is isotopic through maps of pairs to a…

For any $2\leq n\leq \infty$, we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group $\Bbb F_n$. These actions arise as diagonal products between a generalized Bernoulli action and the action $\Bbb…

In this paper we study perturbations of constant cocycles for actions of higher rank semi-simple algebraic groups and their lattices. Roughly speaking, for ergodic actions, Zimmer's cocycle superrigidity theorems implies that the perturbed…

Examples of SL(2, Z) actions on differential graded categories are defined and explored.

We derive new types of $U(1)^n$ Born-Infeld actions based on N=2 special geometry in four dimensions. As in the single vector multiplet (n=1) case, the non--linear actions originate, in a particular limit, from quadratic expressions in the…

We introduce an elementary way of constructing principal (Z_2)^m-bundles over compact smooth manifolds. In addition, we will define a general notion of locally standard (Z_2)^m-actions on closed manifolds for all m>0, and then give a…

We study the classification of group actions on C*-algebras up to equivariant KK-equivalence. We show that any group action is equivariantly KK-equivalent to an action on a simple, purely infinite C*-algebra. We show that a conjecture of…

In this article we show that the quasi-free flows on the Cuntz algebra $\mathcal{O}_2$ are generically classifiable by the inverse temperature of their unique KMS state. Along the way, we show that a large class of quasi-free flows on the…