Related papers: Examples of descent up to nilpotence
Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N = 1 and N = 2). We…
To use evolution algebras to model population dynamics that both allow extinction and introduction of certain gametes in finite generations, nilpotency must be built into the algebraic structures of these algebras with the entire algebras…
A potential scattering theory from deterministic and random $\mathcal{PT}$ collections of particles with gain and loss is introduced and the forms of their structure and pair-structure factors are elucidated. An example relating to light…
A non-nilpotent variety of algebras is almost nilpotent if any proper subvariety is nilpotent. Let the base field be of characteristic zero. It has been shown that for associative or Lie algebras only one such variety exists. Here we…
For a Koszul operad $\mathcal{P}$, there are several existing approaches to the notion of a homotopy between homotopy morphisms of homotopy $\mathcal{P}$-algebras. Some of those approaches are known to give rise to the same notions. We…
We study notions of homotopy in the Newtonian space $N^{1,p}(X;Y)$ of Sobolev type maps between metric spaces. After studying the properties and relations of two different notions we prove a compactness result for sequences in homotopy…
We discuss a very general Kirillov Theory for the representations of certain nilpotent groups which gives a combined view an many known examples from the literature.
Given two nilpotent endomorphisms, we determine when their lattices of hyperinvariant subspaces are isomorphic. The study of the lattice of hyperinvariant subspaces can be reduced to the nilpotent case when the endomorphism has a…
We consider the nilpotent additions to classical trajectories in supersymmetric and nonsupersymmetric theories. The condition of anilpotence of action on some generalized solutions leads to the Witten supersymmetric Lagrangian. The…
We present a construction of left braces of right nilpotency class at most two based on suitable actions of an abelian group on itself with an invariance condition. This construction allows us to recover the construction of a free right…
We give some examples of, and raise some questions on, extensions of semisimple Hopf algebras.
We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. The dynamics for arities of…
In a recent article we introduced a mechanism for producing a presentation of the descent algebra of the symmetric group as a quiver with relations, the mechanism arising from a new construction of the descent algebra as a homomorphic image…
We study the semidirect product of a Lie algebra with a representation up to homotopy and provide various examples coming from Courant algebroids, string Lie 2-algebras, and omni-Lie algebroids. In the end, we study the semidirect product…
We prove a conjecture of J.P. May concerning the nilpotence of elements in ring spectra with power operations, i.e., $H_\infty$-ring spectra. Using an explicit nilpotence bound on the torsion elements in $K(n)$-local $H_\infty$-algebras…
We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley-Lieb…
In this paper we examine various properties/constructions which are known for reductive groups and we do some experiments to see to what extent they generalize to symmetric spaces.
We consider several weaker versions of the notion of conjugacy and orbit equivalence of measure preserving actions of countable groups on probability spaces, involving equivalence of the ultrapower actions and asymptotic intertwining…
For $\Cc$ a $G$-category, we give a condition on a diagram of simplicial sets indexed on $\Cc$ that allows us to define a natural $G$-action on its homotopy colimit, and in some other simplicial sets and categories defined in terms of the…
The calculus of classes and closure operations has proved to be a useful tool in group theory and has led to a deep theory in the study of finite soluble groups. More recently, parallel theories have started to be developed in various…