Related papers: A note on the Akemann-Doner and Farah-Wofsey const…

In this paper we introduce an analog of the tracial Rokhlin property, called the {\emph {projection free tracial Rokhlin property}}, for $C^*$-algebras which may not have any nontrivial projections. Using this we show that if $A$ is an…

Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with $a^2 \in A$ for all $a \in A$. We study noncommutative topology, noncommutative peak sets and peak interpolation, and hereditary subalgebras of Jordan…

It is shown how to construct *-homomorphic quantum stochastic Feller cocycles for certain unbounded generators, and so obtain dilations of strongly continuous quantum dynamical semigroups on C* algebras; this generalises the construction of…

We formulate and prove a non-abelian analog of Deligne's Fixed Part theorem on Hodge classes, revisiting previous work of Jost--Zuo, Katzarkov--Pantev and Landesman--Litt. To this aim we study algebraically isomonodromic extensions of local…

We construct C*-diagonals with connected spectra in all classifiable stably finite C*-algebras which are unital or stably projectionless with continuous scale. For classifiable stably finite C*-algebras with torsion-free $K_0$ and trivial…

Given a connected non-negative unit form we construct an extended affine Lie algebra by giving a Chevalley basis for it. We also obtain this algebra as a quotient of an algebra defined by means of generalized Serre relations by M. Barot, D.…

In previous work, the authors showed that the C*-algebra C*(\Lambda) of a row-finite higher-rank graph \Lambda with no sources is simple if and only if \Lambda is both cofinal and aperiodic. In this paper, we generalise this result to…

Some mathematical questions relating to Coset Conformal Field Theories (CFT) are considered in the framework of Algebraic Quantum Field Theory as developed previously by us. We consider the issue of fixed point resolution in the diagonal…

For a compact Hausdorff space $X$, the space $SC(X\times X)$ of separately continuous complex valued functions on $X$ can be viewed as a $C^*$-subalgebra of $C(X)^{**}\overline\otimes C(X)^{**}$, namely those elements which slice into…

In this paper, we construct new models for the Anderson duals $(I\Omega^G)^*$ to the stable tangential $G$-bordism theories and their differential extensions. The cohomology theory $(I\Omega^G)^*$ is conjectured by Freed and Hopkins [FH21]…

For an action of a finite group on a C*-algebra, we present some conditions under which properties of the C*-algebra pass to the crossed product or the fixed point algebra. We mostly consider the ideal property, the projection property,…

We extend known results about commutative $C^*$-algebras generated Toeplitz operators over the unit ball to the supermanifold setup. This is obtained by constructing commutative $C^*$-algebras of super Toeplitz operators over the super ball…

Consider the differential forms $A^*(L)$ on a Lagrangian submanifold $L \subset X$. Following ideas of Fukaya-Oh-Ohta-Ono, we construct a family of cyclic unital curved $A_\infty$ structures on $A^*(L),$ parameterized by the cohomology of…

Let $A$, $A'$ be separable $C^*$-algebras, $B$ a stable $\sigma$-unital $C^*$-algebra. Our main result is the construction of the pairing $[[A',A]]\times\operatorname{Ext}^{-1/2}(A,B)\to\operatorname{Ext}^{-1/2}(A',B)$, where $[[A',A]]$…

For each $\alpha \in (0,1)$, $A_\alpha$ denotes the universal $C^*$-algebra generated by two unitaries $u$ and $v$, which satisfy the commutation relation $uv=\exp (2\pi i\alpha)vu$. We consider the order four automorphism $\sigma$ of…

We introduce diagonal comparison, a regularity property of diagonal pairs where the sub-C*-algebra has totally disconnected spectrum, and establish its equivalence with the concurrence of strict comparison of the ambient C*-algebra and…

We present a $C^*$-algebra which is naturally associated to the $ax+b$-semigroup over $\mathbb N$. It is simple and purely infinite and can be obtained from the algebra considered by Bost and Connes by adding one unitary generator which…

Let $F$ be the Fibonacci matrix $ \bigl[\begin{smallmatrix} 1 & 1 1 & 0 \\ \end{smallmatrix}\bigr] $. The Fibonacci Dyck shift is a subshsystem of the Dyck shift $D_2$ constrained by the matrix $F$. Let ${{\frak L}^{Ch(D_F)}}$ be a…

The idea of a line bundle in classical geometry is transferred to noncommutative geometry by the idea of a Morita context. From this we can construct Z and N graded algebras, the Z graded algebra being a Hopf-Galois extension. A…

We use the theory of reduced determinant functors from [24] to give a new, computationally useful, description of the relative $K_0$-groups of orders in finite dimensional separable algebras that need not be commutative. By combining this…