Related papers: Linear Map of $D$-Algebra

Given a smooth curve with weighted marked points, the Abel-Jacboi map produces a line bundle on the curve. This map fails to extend to the full boundary of the moduli space of stable pointed curves. Using logarithmic and tropical geometry,…

Let X be a pointed connected simplicial set with loop group G. The linearisation map in K-theory as defined by Waldhausen uses G-equivariant spaces. This paper gives an alternative description using presheaves of sets and abelian groups on…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…

Let G be a finite group and let p be a prime. A module for G over a field of characteristic p is called algebraic if it satisfies a polynomial, with addition and multiplication given by direct sum and tensor product. In some sense, having…

It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the…

In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian category, which for the sake of…

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

Steinberg's tensor product theorem shows that for semisimple algebraic groups the study of irreducible representations of higher Frobenius kernels reduces to the study of irreducible representations of the first Frobenius kernel. In the…

We study modules for the divided power algebra $D$ in a single variable over a commutative noetherian ring $k$. Our first result states that $D$ is a coherent ring. In fact, we show that there is a theory of Gr\"obner bases for finitely…

The goal of this paper is to present an algebraic approach to the basic results of the theory of linear recurrence relations. This approach is based on the ideas from the theory of representations of one endomorphisms (a special case of…

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

For a rational map $\phi: X \to G$ from a normal algebraic variety $X$ to a commutative algebraic group $G$, we define the modulus of $\phi$ as an effective divisor on $X$. We study the properties of the modulus. This work generalizes the…

In \cite{rupel3},the authors defined algebra homomorphisms from the dual Ringel-Hall algebra of certain hereditary abelian category $\mathcal{A}$ to an appropriate $q$-polynomial algebra. In the case that $\mathcal{A}$ is the representation…

Let R be a commutative ring with unity, M a module over R and let S be a G-set for a finite group G. We define a set MS to be the set of elements expressed as the formal finite sum of the form similar to the elements of group ring RG. The…

We consider the structure of algebra of operators, acting in $n-$fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its…

In physics, Lie groups represent the algebraic structure that describes symmetry transformations of a given system. Then, the descending Lie algebra of those groups are necessarily real. In most cases, the complexification of those Lie…

Hereunder we continue the study of the representation theory of the algebra of permutation operators acting on the $n$-fold tensor product space, partially transposed on the last subsystem. We develop the concept of partially reduced…

Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional…

In this article, we present the basic definitions of modules and Lie semialgebras over semirings with a negation map. Our main example of a semiring with a negation map is ELT algebras, and some of the results in this article are formulated…

In this paper, we introduce product interactions, an algebraic formalism in which neural network layers are constructed from compositions of a multiplication operator defined over suitable algebras. Product interactions provide a principled…