We present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. When a certain commutative subalgebra is finitely generated over an algebraically closed field we obtain a classification of a class of locally finite simple weight modules as those induced from simple modules over a subalgebra isomorphic to a tensor product of noncommutative to...

We introduce the concept of a connected logic (over S4) and show that each connected logic with the finite model property is the logic of a subalgebra of the closure algebra of all subsets of the real line R, thus generalizing theMcKinsey-Tarski theorem.As a consequence,weobtain that each intermediate logicwith thefinitemodel property is the logic of a subalgebra of the Heyting algebra of all o...

The dual Steenrod algebra has a canonical subalgebra isomorphic to the homology of the Brown–Peterson spectrum. We will construct a secondary operation in mod-2 homology and show that this canonical subalgebra is not closed under it. This allows us to conclude that the 2-primary Brown–Peterson spectrum does not admit the structure of an En -algebra for any n ≥ 12, answering a question of May in...

In recent work, various algebras of stable degree zero operations in p-local K-theory were described explicitly [5]. The elements are certain infinite sums of Adams operations. Here we show how to make sense of the same expressions for MU(p) and BP , thus identifying the “Adams subalgebra” of the algebras of operations. We prove that the Adams subalgebra is the centre of the ring of degree zero...

‎Let $mathcal{A}$ be a commutative Banach algebra and $mathscr{X}$ be a left Banach $mathcal{A}$-module‎. ‎We study the set‎ ‎${rm Dec}_{mathcal{A}}(mathscr{X})$ of all elements in $mathcal{A}$ which induce a decomposable multiplication operator on $mathscr{X}$‎. ‎In the case $mathscr{X}=mathcal{A}$‎, ‎${rm Dec}_{mathcal{A}}(mathcal{A})$ is the well-known Apostol algebra of $mathcal{A}$‎. ‎We s...

We represent a classical Maxwell-Bloch equation and related to it positive part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is given by an infinitesimal action of a nilpotent subalgebra n+ of affine Lie algebra ŝl2 on a Maxwell-Bloch phase space treated as a homogeneous space of n+. A space of local integrals of motion is described using cohomology methods. We show t...

This paper is a review of results on generalized Harish-Chandra modules in the framework of cohomological induction. The main results, obtained during the last 10 years, concern the structure of the fundamental series of (g, k)−modules, where g is a semisimple Lie algebra and k is an arbitrary algebraic reductive in g subalgebra. These results lead to a classification of simple (g, k)−modules o...

The Peterson-Thom conjecture asserts that any diffuse, amenable subalgebra of a free group factor is contained in unique maximal subalgebra. This motivated by related results Popa's deformation/rigidity theory and Peterson-Thom's on L^{2}-Betti numbers. We present an approach to this terms so-called strong convergence random matrices formulating which natural generalization the Haagerup-Thorbjo...

We introduce what we call the principal subalgebra of a lattice vertex (super) algebra associated to an arbitrary Z-basis of the lattice. In the first part (to appear), the second author considered the case of positive bases and found a description of the principal subalgebra in terms of generators and relations. Here, in the most general case, we obtain a combinatorial basis of the principal s...

In this paper we study subalgebras A of the algebra D(X) of differential operators on a smooth variety X which are big in the following sense: using the order of a differential operator, the ring D(X) is equipped with a filtration. Its associated graded algebra D(X) is commutative and can be regarded as the set of regular functions on the cotangent bundle ofX . The subalgebra A inherits a filtr...