相关论文: On the Descending Central Series of Higher Commuta…
We develop the basic properties of the higher commutator for congruence modular varieties.
We give an accessible introduction into the theory of lower central series of associative algebras, exhibiting the interplay between algebra, geometry and representation theory that is characteristic for this subject, and to discuss some…
We characterize characteristic polynomials of elements in a central simple algebra. We also give an account for the theory of rational canonical forms for separable linear transformations over a central division algebra, and a description…
A general method for calculating or constructing lower central factors of groups is presented. {\it Relative basic commutators} are defined.
In a general algebraic setting, we state some properties of commutators of reflexive admissible relations.
Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit…
We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…
The commutator calculus is one of the basic tools in group theory. However, its extension to the non-associative context, based on the usual definition of the lower central series of a loop, is not entirely satisfactory. Namely, the graded…
There is a relatively well-known description of the algebra of (higher order) left differential operators on commutative algebras. This note gives a construction of similar flavor for algebras of differential operators on not necessarily…
We establish simple combinatorial descriptions of the radical and irreducible representations specifically for the descent algebra of a Coxeter group of type $D$ over any field.
The characters of the unitarizable highest weight modules over the N=2 superconformal algebras are presented. This is a slightly extended version of an Encyclopedia entry.
A commutative order in a central simple algebra over a number field is said to be selective if it embeds in some, but not all, the maximal orders in the algebra. We completely characterize selective orders in central division algebras, of…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
The behavior of nilpotents can reveal valuable information about the algebra. We give a simple proof of a classic result that a finite ring is commutative if all its nilpotents lie in the center.
We study centralizers in certain algebras with valuation in order to generalize results by Hellstr\"{o}m and Silvestrov on centralizers in graded algebras. We prove that the centralizer of an element in the studied algebras is a free module…
Higher derivations on an associative algebra generalizes higher order derivatives. We call a tuple consisting of an algebra and a higher derivation on it by an AssHDer pair. We define a cohomology for AssHDer pairs with coefficients in a…
In this paper we discuss some results related to commuting ordinary differential operators of rank greater than one.
Recollements of derived module categories are investigated, using a new technique, ladders of recollements, which are mutation sequences. The position in the ladder is shown to control whether a recollement restricts from unbounded to…
We study whether a unital associative algebra $ A $ over a field admits a decomposition of the form $A = Z(A) + [A,A]$ where $ Z(A) $ is the center of $ A $ and $ [A,A] $ denotes the additive subgroup of $A$ generated by all additive…
This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications.