Related papers: Cancellative Convex Semilattices
The cone of lower semicontinuous traces is studied with a view to its use as an invariant. Its properties include compactness, Hausdorffness, and continuity with respect to inductive limits. A suitable notion of dual cone is given. The cone…
We investigate categorical and amalgamation properties of the functor Idc assigning to every partially ordered abelian group G its semilattice of compact ideals Idc G. Our main result is the following. Theorem 1. Every diagram of finite…
In this paper, a new invariant was built towards the classification of separable C*-algebras of real rank zero, which we call latticed total K-theory. A classification theorem is given in terms of such an invariant for a large class of…
Let X be a (connected and reduced) complex space. A q-collar of X is a bounded domain whose boundary is a union of a strongly q-pseudoconvex, a strongly q-pseudoncave and two flat (i.e. locally zero sets of pluriharmonic functions)…
We introduce a notion of covering dimension for Cuntz semigroups of C*-algebras. This dimension is always bounded by the nuclear dimension of the C*-algebra, and for subhomogeneous C*-algebras both dimensions agree. Cuntz semigroups of…
It is shown that the Cuntz semigroup of a space with dimension at most two, and with second cohomology of its compact subsets equal to zero, is isomorphic to the ordered semigroup of lower semicontinuous functions on the space with values…
Let End(V) denote the ring of all linear transformations of an arbitrary k-vector space V over a field k. We define a subset X of End(V) to be "triangularizable" if V has a well-ordered basis such that X sends each vector in that basis to…
Algebras generated by strictly positive matrices are described up to similarity, including the commutative, simple, and semisimple cases. We provide sufficient conditions for some block diagonal matrix algebras to be generated by a set of…
We present a concise proof for the supporting hyperplane theorem. We then observe that the proof not only establishes the supporting hyperplane theorem but also extends it to a hyperplane separation theorem for certain non-convex sets. The…
Convex rank tests are partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. Each class consists of the…
In this paper we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by…
We generalize the "facial weak order" of a finite Coxeter group to a partial order on a set of intervals in a complete lattice. We apply our construction to the lattice of torsion classes of a finite-dimensional algebra and consider its…
A real seminormed involutive algebra is a real associative algebra ${\mathcal A}$ endowed with an involutive antiautomorphism $*$ and a submultiplicative seminorm $p$ with $p(a^*) =p(a)$ for $a\in {\mathcal A}$. Then ${\mathop{\tt…
A universal coefficient theorem is proved for C*-algebras over an arbitrary finite T_0-space X which have vanishing boundary maps. Under bootstrap assumptions, this leads to a complete classification of unital/stable real-rank-zero…
Pseudo-effect algebras are partial algebraic structures, that were introduced as a non-commutative generalization of effect algebras. In the present paper, lattice ordered pseudo-effect algebras are considered as possible algebraic…
For any integral lattice $Q$, one can construct a vertex algebra $V_Q$ called a lattice vertex algebra. If $\sigma$ is an automorphism of $Q$ of finite order, it can be lifted to an automorphism of $V_Q$. In this paper we classify the…
We consider simple cusp algebras, that is certain subalgebras of the algebra of holomorphic functions on a disk that are annihilated by some distributions living on a singleton. We determine when these algebras can be holized in two…
We consider commuting squares of finite dimensional von Neumann algebras having the algebra of complex numbers in the lower left corner. Examples include the vertex models, the spin models (in the sense of subfactor theory) and the…
A commutative associative algebra A with an identity over the field of real numbers which has a basis, where all elements are invertible, is considered in the work. Moreover, among matrixes consisting of the structure constants of A, there…
Absolute algebras are a new type of algebraic structures, endowed with a meaningful notion of infinite sums of operations without supposing any underlying topology. Opposite to the usual definition of operadic calculus, they are defined as…