Related papers: Groupoids decomposition, propagation and K-theory
Let $K$ be a complete non-archimedean valuation field of characteristic $0$, with non-trivial valuation, equipped with (possibly multiple) commuting bounded derivations. We prove a decomposition theorem for finite differential modules over…
K-core decomposition is a commonly used metric to analyze graph structure or study the relative importance of nodes in complex graphs. Recent years have seen rapid growth in the scale of the graph, especially in industrial settings. For…
This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann…
I determine the twisted K-theory of all compact simply connected simple Lie groups. The computation reduces via the Freed-Hopkins-Teleman theorem to the CFT prescription, and thus explains why it gives the correct result. Finally I analyze…
We provide descriptions of the Whitehead groups, and the algebraic $K$-theory groups, of the fundamental group of a connected, oriented, closed $3$-manifold in terms of Whitehead groups of their finite subgroups and certain Nil-groups. The…
We compute the $K$-theory groups of the groupoid C$^\ast$-algebra of the chair tiling, using a new method. We use exact sequences of Putnam to compute these groups from the $K$-theory groups of the $AF$-algebras of the substitution and the…
It was shown by Rordam and the second named author that a countable group G admits an action on a compact space such that the crossed product is a Kirchberg algebra if, and only if, G is exact and non-amenable. This construction allows a…
We introduce the notion of (strong) subexponential growth for \'etale groupoids and study its basic properties. In particular, we show that the K-groups of the associated groupoid $L^p$-operator algebras are independent of $p \in…
We describe two crystal structures on set-valued decomposition tableaux. These provide the first examples of interesting "$K$-theoretic" crystals on shifted tableaux. Our first crystal is modeled on a similar construction of Monical,…
Following Hopkins and Singer, we give a definition for the differential equivariant K-theory of a smooth manifold acted upon by a finite group. The ring structure for differential equivariant K-theory is developed explicitly. We also…
In this short paper we generalise a theorem due to Kani and Rosen on decomposition of Jacobian varieties of Riemann surfaces with group action. This generalisation extends the set of Jacobians for which it is possible to obtain an isogeny…
It is well-known that quantum groups are relevant to describe the quantum regime of 3d gravity. They encode a deformation of the gauge symmetries parametrized by the value of the cosmological constant. They appear as a form of…
We address primary decomposition conjectures for knot concordance groups, which predict direct sum decompositions into primary parts. We show that the smooth concordance group of topologically slice knots has a large subgroup for which the…
The book "N-ary Groups" (in Russian) consists of two Parts. It is intended on the one hand as an initial introduction to the theory of n-ary groups, and on the other hand it contains the published results by the author on this subject. At…
We prove a decomposition formula for the dimensional reduction of an extended topological field theory that arises as an orbifold of an equivariant topological field theory. Our decomposition formula can be expressed in terms of a…
In this paper, we compute Tian's $\alpha_{m,k}^{K\times K}$-invariant on a polarized $G$-group compactification, where $K$ denotes a maximal compact subgroup of a connected complex reductive group $G$. We prove that Tian's conjecture (see…
The term Clifford group was introduced in 1998 by D. Gottesmann in his investigation of quantum error-correcting codes. The simplest Clifford group in multiqubit quantum computation is generated by a restricted set of unitary Clifford gates…
Based on the localization algebras of Yu, and their subsequent analysis by Qiao and Roe, we give a new picture of KK-theory in terms of time-parametrized families of (locally) compact operators that asymptotically commute with appropriate…
This is a short, self-contained expository survey, focused on algebraic and analytic aspects of quantum groups. Topics covered include the definition of ``quantum group,'' the Yang-Baxter equation, quantized universal enveloping algebras,…
In 1999, Brylinski and Zhang computed the complex equivariant K-theory of the conjugation self-action of a compact, connected Lie group with torsion-free fundamental group. In this note we show it is possible to do so in under a page.