Related papers: Definite orders with locally free cancellation

We present several enumeration results holding in sets of words called neutral and which satisfy restrictive conditions on the set of possible extensions of nonempty words. These formulae concern return words and bifix codes. They…

For a commutative Noetherian local ring we define and study the class of modules having reducible complexity, a class containing all modules of finite complete intersection dimension. Various properties of this class of modules are given,…

In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.

Let $K$ be a global function field together with a place $\infty$, and $A$ the subring of functions regular outside $\infty$. In this paper we present an effective method to evaluate the (locally free) class number of an arbitrary…

All simple weight modules with finite dimensional weight spaces over affine Lie algebras are classified.

We build on our previous paper \cite{constructive} by using the general method introduced there in conjunction with invariant theory. This yields quantifier elimination results for the classical quaternions, octonions, as well as other…

In this paper, we give the complete structures of the equivalence canonical form of four matrices over an arbitrary division ring. As applications, we derive some practical necessary and sufficient conditions for the solvability to some…

Let $A$ be a real quadratic order of discriminant $p$ or $4p$ with a prime $p$. In this paper we classify all proper totally imaginary quadratic $A$-orders $B$ with index $w(B)=[B^\times: A^\times]>1$. We also calculate numerical invariants…

We give a generalization of Gelfand's criterion on the commutativity of Hecke algebras for Gelfand pairs and multiplicity-free triples over algebraically closed fields of arbitrary characteristic. Using more lenient versions of projectivity…

This paper addresses a construction of new $q-$Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three-term recursive relation as well as the second-order…

The paper presents a classification of quadratic extension algebras, also known as algebras of degree 2, as well as several characterizations of quaternion algebras over a field (of characteristic not 2). The presentation is not restricted…

We study permutation invariant oscillator algebras and their Fock space representations using three equivalent techniques, i.e. (i) a normally ordered expansion in creation and annihilation operators, (ii) the action of annihilation…

In this paper, we first present a classification theorem of infinite-dimensional simple Novikov algebras over an algebraically closed field with characteristic 0. Then we classify all the irreducible modules of a certain…

For any positive integer $n$, $\mathcal{A}_n$ is the class of all groups $G$ such that, for $0\leq i\leq n$, $H^i(\hat{G},A)\cong H^i(G,A)$ for every finite discrete $\hat{G}$-module $A$. We describe certain types of free products with…

We present some Zermelo-Fraenkel consistency results regarding bi-orderability of groups, as well as a construction of groups with Conradian orders whose every action on metric spaces has bounded orbits. A classical consequence of the…

We study the correspondence assigning the vertices of a certain quotient of the local Bruhat-Tits tree for the general linear group over a global function field, to conjugacy classes of maximal orders in some quaternion algebras. The…

We give an algebraic quantifier elimination algorithm for the first-order theory over any given finite field using Gr\"obner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite…

Two extension problems are solved. First, the class of locally matricial algebras over an arbitrary field is closed under extensions. Second, the class of locally finite dimensional semisimple algebras over a fixed field is closed under…

Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case…

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.