2 citations · 3 across the 14 of their papers we have counts for
19 papers
Growth functions of algebras and an application to Leavitt path algebras
João Schwarz, Alfilgen Sebandal
In this paper, we consider three growth functions of algebras: the Gelfand-Kirillov dimension, superdimension, and entropy -- as well as a variation of the latter successfully used…
On Locally Finite Derivations in Ore Extensions
R. Baltazar, A. Bianchi, M. Veloso +1
Let be an algebraically closed field of characteristic zero. We classify the locally finite derivations of arbitrary Ore extensions of , thus extending van den Es…
Irreducible non-holonomic modules for rational Cherednik algebras
Felipe Albino dos Santos, João Schwarz
Let be an algebraically closed field of characteristic zero and let be the -th Weyl algebra. We prove that for every complex reflection group …
Graded identities of the first Weyl algebra and its generalizations
V. Futorny, P. Koshlukov, J. Schwarz
We study the graded polynomial identities of the first Weyl algebra over an infinite field. The algebra satisfies no ordinary polynomial identities in characteristic 0.…
Characteristic free Galois rings and generalized Weyl algebras
Joao Schwarz
This paper develops from scratch a theory of Galois rings and orders over arbitrary fields. Our approach is different from others in the literature in that there is no non-modulari…
Galois Rings: Ring-Theoretic Properties and Applications to Coulomb Branches and Affine Hecke Algebras
Vyacheslav Futorny, Jonas T. Hartwig, Erich C. Jauch +1
Galois rings and Galois orders, introduced by Futorny and Ovsienko, are realized as subrings of fixed subrings of skew group (or monoid) rings and have numerous applications in the…
A note on the definition of derived functors
João Schwarz
The purpose of this note is to consider in detail the construction of derived functors. The classical construction, such as in Cartan-Eilenberg or Grothendieck, is clarified, and i…
Hilbert-Samuel Polynomials for Algebras with Special Filtrations
Jonas T. Hartwig, Erich C. Jauch, João Schwarz
The notion of multiplicity of a module first arose as consequence of Hilbert's work on commutative algebra, relating the dimension of rings with the degree of certain polynomials.…
Generalizations of noncommutative Noether's problem
João Schwarz
Noether's problem is classical and very important problem in algebra. It is an intrinsically interesting problem in invariant theory, but with far reaching applications in the sutd…
Harish-Chandra modules and Galois orders revisited
João Schwarz
The main subject of study of this paper are general properties of HarishChandra algebras and modules with respect wito a pair of algebra and subalgebra, with special focus on the t…
On rational twisted generalized Weyl algebra
Natalia Golovashchuk, João Schwarz
The aim of this work is to investigate the structure of some skew twisted algebras, when the coefficient ring is a localization of the polynomial ring over the field of characteris…
Holonomic modules for rings of invariant differential operators
Vyacheslav Futorny, João Schwarz
We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite g…
Gelfand-Kirillov conjecture as a first-order formula
Hugo Luiz Mariano, João Schwarz
Let be a (reduced) root system. Let be an algebraically closed field of zero characteristic, and consider the corresponding semisimple Lie algebra $\mathfrak{g}_{\…
LD-stability for Goldie rings
Vyacheslav Futorny, João Schwarz, Ivan Shestakov
The lower transcendence degree, introduced by J. J Zhang, is an important non-commutative invariant in ring theory and non-commutative geometry strongly connected to the classical…
A Poisson Analogue of Noether's Problem
João Schwarz
In this paper we show that the Poisson analogue of the Noether's Problem has a positive solution for essentially all finite symplectic reflection groups - the analogue of complex r…
Noncommutative Noether's Problem vs Classical Noether's Problem
Vyacheslav Futorny, João Schwarz
We address the Noncommutative Noether's Problem on the invariants of Weyl fields for linear actions of finite groups. We prove that if the variety An(k)/G is rational then the Nonc…
Quantum Linear Galois Algebras
V. Futorny, J. Schwarz
We define a class of quantum linear Galois algebras which include the universal enveloping algebra Uq(gln), the quantum Heisenberg Lie algebra and other quantum orthogonal Gelfand-…
Algebras of invariant differential operators
Vyacheslav Futorny, Joao Schwarz
We prove that an invariant subalgebra A_n^W of the Weyl algebra A_n is a Galois order over an adequate commutative subalgebra Γwhen W is a two-parameters irreducible unitary reflec…
Noncommutative Noether's problem for complex reflection groups
Farkhod Eshmatov, Vyacheslav Futorny, Sergiy Ovsienko +1
We solve the noncommutative Noether's problem for the reflection groups by showing that the skew field of the invariants of the Weyl algebra under the action of any reection group…