Related papers: Endomorphisms of B(H)

Given any matrix B in SL(2,Z), we will describe an algorithm that provides at least one elliptic fibration over the disk, relatively minimal and Lefschetz, within each topological equivalence class, whose total monodromy is the conjugacy…

We describe the geometry of conjugation within any split subgroup $H$ of the full isometry group $G$ of $n$-dimensional Euclidean space. We prove that for any $h \in H$, the conjugacy class $[h]_H$ of $h$ is described geometrically by the…

We prove that simple, separable, monotracial UHF $L^{p}$-operator algebras are not classifiable up to (complete) isomorphism using countable structures, such as K-theoretic data, as invariants. The same assertion holds even if one only…

This paper determines all the possible endomorphism algebras for polarizable Q-Hodge structures of type (n,0,...,0,n). This generalizes the classification of the possible endomorphism algebras of abelian varieties by Albert and Shimura. As…

We set up a homological algebra for N-complexes, which are graded modules together with a degree -1 endomorphism d satisfying d^N=0. We define Tor- and Ext-groups for N-complexes and we compute them in terms of their classical counterparts…

We study the categories of singularities coming from Landau-Ginzburg models given by the invertible polynomials. Such categories appear on the B-side of the Berglund-H\"ubsch mirror symmetry. We provide an efficient method of computing…

Previous noncommutative Bohnenblust--Hille (BH) inequalities addressed operator decompositions in the tensor-product space $M_2(\mathbb{C})^{\otimes n}$; \emph{i.e.,} for systems of qubits \cite{HCP22,VZ23}. Here we prove noncommutative BH…

This paper gives an elementary introduction to noncommutative deformations of modules. The main results of this deformation theory are due to Laudal. Let k be an algebraically closed (commutative) field, let A be an associative k-algebra,…

We investigate PBW deformations H of k[x,y]#G where G is the cyclic group of order p and k also has characteristic p; in these deformations, [x,y] takes a value in kG. These algebras are versions of symplectic reflection algebras that only…

Let $H$ be a Hopf algebra, $A/B$ be an $H$-Galois extension. Let $D(A)$ and $D(B)$ be the derived categories of right $A$-modules and of right $B$-modules respectively. An object $M^\cdot\in D(A)$ may be regarded as an object in $D(B)$ via…

Let $\mathbf{k}$ be an algebraically closed field. Recently, K. Erdmann classified the symmetric $\mathbf{k}$-algebras $\Lambda$ of finite representation type such that every non-projective module $M$ has period dividing four. The goal of…

We study a class of representations of the Cuntz algebras O_N, N=2,3,..., acting on L^2(T) where T=R/2\pi Z. The representations arise in wavelet theory, but are of independent interest. We find and describe the decomposition into…

We realise non-unitary fusion categories using subfactor-like methods, and compute their quantum doubles and modular data. For concreteness we focus on generalising the Haagerup-Izumi family of Q-systems. For example, we construct…

We study the noncommutative differential geometry of the algebra of endomorphisms of any SU(n)-vector bundle. We show that ordinary connections on such SU(n)-vector bundle can be interpreted in a natural way as a noncommutative 1-form on…

Let $G$ be a simple algebraic group over an algebraically closed field $k$ of characteristic $p$. The classification of the conjugacy classes of unipotent elements of $G(k)$ and nilpotent orbits of $G$ on $\operatorname{Lie}(G)$ is…

We consider a category whose morphisms are bordisms of $n$-dimensional pseudomanifolds equipped with a certain additional structure (coloring). On the other hand, we consider the product $G$ of $(n+1)$ copies of infinite symmetric group. We…

Let $H$ be a Hopf algebra over a field $k$, and $A$ an $H$-comodule algebra. The categories of comodules and relative Hopf modules are then Grothendieck categories with enough injectives. We study the derived functors of the associated Hom…

A unital $C^*$-algebra is called $N$-subhomogeneous if its irreducible representations are finite dimensional with dimension at most $N$. We extend this notion to operator systems, replacing irreducible representations by boundary…

We consider the group G of R-automorphisms of the polynomial ring R[x] especially in the case where R is the ring of integers modulo n. We describe conjugacy classes in G, and in the case where n = 4, we describe more explicitly the…

We provide a group-theoretical classification of the entangled states of N identical particles. The connection between quantum entanglement and the exchange symmetry of the states of N identical particles is made explicit using the duality…