Let q be a Lie algebra over field k and p,p˜∈k[t] two different normalised polynomials of degree n⩾2. As vector spaces, both quotient algebras q[t]/(p) q[t]/(p˜) can identified with W=q⋅1⊕qt¯⊕…⊕qt¯n−1. If deg⁡(p−p˜)⩽1, then the brackets [,]p, [,]p˜ induced on W by p p˜, respectively, are compatible. Making use Lenard–Magri scheme, we construct subalgebra Z=Z(p,p˜)⊂S(W)q⋅1 such that {Z,Z}p={Z,Z}...

Based on cosmogenic 10Be and 26Al analyses in 15 individual detrital quartz pebbles (16–21 mm) and cosmogenic 10Be in amalgamated medium sand (0.25–0.50 mm), all collected from the outlet of the upper Gaub River catchment in Namibia, quartz pebbles yield a substantially lower average denudation rate than those yielded by the amalgamated sand sample. 10Be and 26Al concentrations in the 15 indivi...

Abstract: Let X be a Banach space. We define the concept of a bi-parameter semigroup on X and its first and second generators. We also study bi-parameter semigroups on Banach algebras. A relation between uniformly continuous bi-parameter semigroups and σ-derivations is also established. It is proved that if {αt,s}t,s 0 is a uniformly continuous bi-parameter semigroup on a Banach algebra X , who...

The concept of a Hopf algebra originated in topology. Classically, Hopf algebras are defined on the basis of unital modules over commutative, unital rings. The intention of the present work is to study Hopf algebra formalism (§1.2) from a universal-algebraic point of view, within the context of entropic varieties. In an entropic variety, the operations of each algebra are homomorphisms, and ten...

We extend Makkai’s proof of strong amalgamation (push-outs of monos along arbitrary maps are monos) from the category of Heyting algebras to a class which includes the categories of symmetric bounded distributive lattices, symmetric Heyting algebras, Heyting modal S4-algebras, Heyting modal bi-S4-albegras, and Lukasiewicz n-valued algebras. We also extend and improve Pitt’s proof that strong am...

We study L-Betti numbers for von Neumann algebras, as defined by D. Shlyakhtenko and A. Connes in [4]. We give a definition of Lcohomology and show how the study of the first L-Betti number can be related to the study of derivations with values in a bi-module of affiliated operators. We show several results about the possibility of extending derivations from sub-algebras and about uniqueness of...

We define quantum bi-Hamiltonian systems, by analogy with the classical case, as derivations in operator algebras which are inner derivations with respect to two compatible associative structures. We find such structures by means of the associative version of Nijenhuis tensors. Explicit examples, e.g. for the harmonic oscillator, are given.

We classify indecomposable commutative separable (special Frobenius) algebras and their local modules in (untwisted) group-theoretical modular categories. This gives a description of modular invariants for grouptheoretical modular data. As a bi-product we provide an answer to the question when (and in how many ways) two group-theoretical modular categories are equivalent as ribbon categories.