Related papers: The Scheme of Monogenic Generators I: Representabi…

For a left coherent ring A with every left ideal having a countable set of generators, we show that the coderived category of left A-modules is compactly generated by the bounded derived category of finitely presented left A-modules…

We study the parametrizations of simple modules provided by the theory of basic sets for all finite Weyl groups. In the case of type B, we show the existence of basic sets for the matrices of constructible representations. Then we study…

We investigate the representation theory of the Temperley-Lieb algebra, $TL_n(\delta)$, defined over a field of positive characteristic. The principle question we seek to answer is the multiplicity of simple modules in cell modules for…

Let $K$ be a field, $V$ a $K$-vector space with basis $e_1,\ldots,e_n$, and $E$ the exterior algebra of $V$. To a given monomial ideal $I\subsetneq E$ we associate a special monomial ideal $J$ with generators in the same degrees as those of…

For a cubic number field $L$, we consider the $\mathbb{Z}$-order in $L$ of the form $\mathbb{Z}[\alpha]$, where $\alpha$ is a root of a polynomial of the form $x^3-ax+b$ and $a,b\in\mathbb{Z}$ are integers such that $v_p(a)\leq 2$ or…

We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary…

In this paper, we introduce a new notion called the \textit{set of missing generators} $\mathcal{M}(g)$ for a generator (or primitive element) $g$ of the cyclic group $\mathbb{Z}_p^*$, where $p$ is an odd prime. The cardinality of…

Let $M$ be a finitely generated module over a Noetherian local ring. This paper reports, for a given parameter ideal $Q$ for $M$, a criterion for the equality…

We give a new construction of the algebraic $K$-theory of small permutative categories that preserves multiplicative structure, and therefore allows us to give a unified treatment of rings, modules, and algebras in both the input and…

We explore the question concerning the number of distinct resonant algebras depending on the generator content, which consists of the Lorentz generator, translation, and new additional Lorentz-like and translation-like generators. Such…

In this paper, we initiate the study of endomorphisms and modular theory of the graph C*-algebras $\O_{\theta}$of a 2-graph $\Fth$ on a single vertex. We prove that there is a semigroup isomorphism between unital endomorphisms of…

Let $A$ be an algebra over a field $K$ of characteristic zero, let $\d_1, >..., \d_s\in \Der_K(A)$ be {\em commuting locally nilpotent} $K$-derivations such that $\d_i(x_j)=\d_{ij}$, the Kronecker delta, for some elements $x_1,..., x_s\in…

Let M be a finitely generated submodule of a free module over a multivariate polynomial ring with coefficients in a discrete coherent ring. We prove that its module MLT(M ) of leading terms is countably generated and provide an algorithm…

The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…

For a prime number p, we construct a generating set for the ring of invariants for the p+1 dimensional indecomposable modular representation of a cyclic group of order p^2. We then use the constructed invariants to describe the…

Shapovalov elements $\theta_{\beta,m}$ are special elements in a Borel subalgebra of a classical or quantum universal enveloping algebra parameterized by a positive root $\beta$ and a positive integer $m$. They relate the canonical…

It is natural to study octonion Hilbert spaces as the recently swift development of the theory of quaternion Hilbert spaces. In order to do this, it is important to study first its algebraic structure, namely, octonion modules. In this…

The first part of this dissertation defines "dependently typed algebraic theories", which are a strict subclass of the generalised algebraic theories (GATs) of Cartmell. We characterise dependently typed algebraic theories as finitary…

Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…

Let $A$ be a $C^*$-algebra. Let $E$ and $F$ be Hilbert $A$-modules with $E$ being full. Suppose that $\theta : E\to F$ is a linear map preserving orthogonality, i.e., $<\theta(x), \theta(y) > = 0$ whenever $<x, y > = 0$. We show in this…