Related papers: Relative Cancellation
We study relative Cohn path algebras, also known as Leavitt-Cohn path algebras, and we realize them as partial skew group rings (to do this we prove uniqueness theorems for relative Cohn path algebras). Furthermore, given any graph $E$ we…
We construct a geometric system from which the Hall algebra can be recovered. This system inherently satisfies higher associativity conditions and thus leads to a categorification of the Hall algebra. We then suggest how to use this…
A quantitative form of the Nullity Theorem is presented, which establishes a linear relation between the singular values of the two submatrices involved in the theorem up to the first order. The theorem is then extended to function spaces…
Let $F$ be an algebraically closed field of positive characteristic and let $R$ be a finitely generated $F$-algebra with a filtration with the property that the associated graded ring of $R$ is an integral domain of Krull dimension two. We…
This is the first installment of an exposition of an ACL2 formalization of elementary linear algebra, focusing on aspects of the subject that apply to matrices over an arbitrary commutative ring with identity, in anticipation of a future…
We study rings of real-valued continuous functions in terms of pseudocomplementation conditions on various lattices attached to their prime spectrum. We fully characterize pseudocomplementation in all cases and have an almost complete…
In this work, we obtain contraction results for a class of diagrams of ring morphisms which strictly includes the ones obtained by Lipman. Further, we present some applications on quotient and in the changing of the base ring in the…
Holonomy R-matrices parametrized by finite-dimensional representations are constructed for quantized universal enveloping algebras of simple Lie algebras at roots of 1.
The mechanism by which gauge and gravitational anomalies cancel in certain string theories is reviewed. The presentation is aimed at theorists who do not necessarily specialize in string theory.
We characterize the relative prismatic cohomology of Bhatt and Scholze by a universal property by endowing it with the additional structure of a ``derived $\delta$-ring". This involves introducing an analogue of prismatic envelopes in the…
We define several versions of the cohomology ring of an associative algebra. These ring structures unify some well known operations from homological algebra and differential geometry. They have some formal resemblance with the quantum…
It seems that the index theory for non-compact spaces has found its ultimate formulation in realm of coarse spaces and $K$-theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and…
We introduce partial group algebras with relations in a purely algebraic framework. Given a group and a set of relations, we define an algebraic partial action and prove that the resulting partial skew group ring is isomorphic to the…
Adapting a claim of M. Kracht, we establish a characterization of the typable partial applicative algebras.
We give a purely algebraic treatment of reduction theory for connections over the formal punctured disc. Our proofs apply to arbitrary connected linear algebraic groups over an algebraically closed field of characteristic 0. We also state…
We study rational Cherednik algebras over an algebraically closed field of positive characteristic. We first prove several general results about category O, and then focus on rational Cherednik algebras associated to the general and special…
We study the quantum Hamiltonian reduction for affine superalgebras in the twisted case. This leads to a general representation theory of all superconformal algebras, including the twisted ones (like the Ramond algebra). In particular, we…
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.
Two $(p,q)$-Laplace transforms are introduced and their relative properties are stated and proved. Applications are made to solve some $(p,q)$-linear difference equations.
An algebra of germs of real functions is generalised quasianalytic if to each element of the algebra we can associate, injectively, a power series with nonnegative real exponents. We prove a quantifier elimination and a rectilinearisation…