Related papers: Divisorial algebras and modules on schemes
We analyze cyclic cell modules over walled Brauer algebra in terms of a certain normal form. The latter allows us to decompose the algebra into the generating set and annihilator ideal of a certain cyclic vector. In addition, we show that…
We characterize the canonical algebras such that for all dimension vectors of homogeneous modules the corresponding module varieties are complete intersections (respectively, normal). We also investigate the sets of common zeros of…
The volume of a Cartier divisor on a projective variety is a nonnegative real number that measures the asymptotic growth of sections of multiples of the divisor. It is known that the set of these numbers is countable and has the structure…
We give an alternative proof to the fact that if the square of the infinite radical of the module category of an Artin algebra is equal to zero then the algebra is of finite type by making use of the theory of postprojective and…
We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…
We discuss the log minimal model theory for log surfaces. We show that the log minimal model program, the finite generation of log canonical rings, and the log abundance theorem for log surfaces hold true under assumptions weaker than the…
A classification of multiplication modules over multiplication rings with finitely many minimal primes is obtained. A characterisation of multiplication rings with finitely many minimal primes is given via faithful, Noetherian, distributive…
We describe the heart of the canonical $t$-structure on the perfect derived category of a strictly positive graded algebra as the module category over the quadratic dual. Applying this result we obtain examples showing new phenomena on…
Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation…
This article begins the study of irreducible maps involving finite-dimensional uniserial modules over finite-dimensional associative algebras. We work on the classification of irreducible maps between two uniserials over triangular…
This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules. We adopt the constructive point of view, with which all existence theorems have an explicit algorithmic…
An algorithm is described to compute the canonical basis of an irreducible module over a quantized enveloping algebra of a finite-dimensional semisimple Lie algebra. The algorithm works for modules that are constructed as a submodule of a…
A self-contained introduction to infinite dimensional representations over a tame hereditary algebra is provided, assuming a basic knowledge of the category of finite dimensional representations. This includes a complete description of all…
In this article the quantized matrix algebras as in the title have been studied at a root of unity. A full classification of simple modules over such quantized matrix algebras of rank $2$ along with a class of finite dimensional…
We investigate the minimal number of generators $\mu$ and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the…
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
We define a type B analogue of the category of finite sets with surjections, and we study the representation theory of this category. We show that the opposite category is quasi-Grobner, which implies that submodules of finitely generated…
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 paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
Let $L$ be a finite-dimensional Lie algebra over a field of non-zero characteristic and let $S$ be a subalgebra. Suppose that $X$ is a finite set of finite-dimensional $L$-modules. Let $D$ be the category of all finite-dimensional…