Related papers: Topology of eigenspace posets for unitary reflecti…
In the present survey paper, we present several new classes of Hochster's spectral spaces "occurring in nature", actually in multiplicative ideal theory, and not linked to or realized in an explicit way by prime spectra of rings. The…
This is an expository book on unitary representations of topological groups, and of several dual spaces, which are spaces of such representations up to some equivalence. The most important notions are defined for topological groups, but a…
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…
S. Gudder and, later, S. Pulmanova and E. Vincekova, have studied in two recent papers a certain ordering of bounded self-adjoint operators on a Hilbert space. We present some further results on this ordering and show that some structure…
A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially…
A natural topology on the space of left orderings of an arbitrary semi-group is introduced. It is proved that this space is compact and that for free abelian groups it is homeomorphic to the Cantor set. An application of this result is a…
We develop a new method to compute the homology groups of finite topological spaces (or equivalently of finite partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding…
A poset-stratified space is a pair $(S, S \xrightarrow \pi P)$ of a topological space $S$ and a continuous map $\pi: S \to P$ with a poset $P$ considered as a topological space with its associated Alexandroff topology. In this paper we show…
The second author gave a formula for the elements of the enveloping algebra of a Lie superalgebra defined by Gorelik under an appropriate unimodularity assumption. We show that this formula is a particular case of a formula for the Jacobian…
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…
A closed real subspace V of a complex Hilbert space H is called standard if V intersects iV trivially and and V + i V is dense in H. In this note we study several aspects of the geometry of the space Stand(H) of standard subspaces. In…
This paper identifies the homotopy theories of topological stacks and orbispaces with unstable global homotopy theory. At the same time, we provide a new perspective by interpreting it as the homotopy theory of `spaces with an action of the…
In this paper we introduce and study the poset of equivalence classes of subgroups of a finite group $G$, induced by the isomorphism relation. This contains the well-known lattice of solitary subgroups of $G$. We prove that in several…
We describe some open problems related to homology representations of subposets of the partition lattice, beginning with questions first raised in Stanley's work on group actions on posets.
The complement of an arrangement A of a finite number of affine hyperplanes in complex n-space has the structure of a poset of spaces indexed by the intersection poset, L(A). The space corresponding to G in L(A) is homotopy equivalent to…
Earlier an arbitrary poset $P$ was proved to be isomorphic to the collection of subsets of a space $M$ with two closures which are closed in the first closure and open in the other. As a space $M$ for this representation an algebraic dual…
By using a lattice characterization of continuous projections defined on a topological vector space E arising from a dual pair, we determine the automorphism group of their orthomodular poset Proj(E) by means of automorphisms and…
We investigate the structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group. We work with square integrable representations, and we show that they are those for which we can construct an…
The notions of reflection, symmetry, and positivity from quantum field theory are shown to induce a duality operation for a general class of unitary representations of Lie groups. The semisimple Lie groups which have this $c$-duality are…
Popov classified crystallographic complex reflection groups by determining lattices they stabilize. These analogs of affine Weyl groups have infinite order and are generated by reflections about affine hyperplanes; most arise as the…