23 citations · 43 across the 33 of their papers we have counts for
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Number of homogeneous components of counterexamples to the Dixmier conjecture
Jorge Guccione, Juan Jose Guccione, Christian Valqui
Assume that and are elements of satisfying . The Dixmier Conjecture for says that they always generate . We show that if is a sum of not mor…
Set-theoretic type solutions of the braid equation
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
In this paper we begin the study of set-theoretic type solution of the braid equation. Our theory includes set-theoretical solutions as basic examples. We show that the relationshi…
On the classification of graded twisted planes
Ricardo Bances, Christian Valqui
We use a representation of a graded twisted tensor product of with in in order to obtain a nearly complete classification of these graded twisted t…
Cleft extensions of weak Hopf algebras
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
In this paper we study the theory of cleft extensions for a weak bialgebra H. Among other results, we determine when two unitary crossed products of an algebra A by H are equivalen…
Twisted tensor products of with
J. Arce, Jorge A. Guccione, Juan J. Guccione +1
We find three families of twisting maps of K^m with K^n. One of them is related to truncated quiver algebras, the second one consists of deformations of the first and the third one…
The starred Dixmier conjecture for
Christian Valqui, Vered Moskowicz
Let be the first Weyl algebra over a characteristic zero field and let be the exchange involution on given by a…
A differential equation for polynomials related to the Jacobian conjecture
Christian Valqui, Jorge Alberto Guccione, Juan José Guccione
We analyze a possible minimal counterexample to the Jacobian Conjecture with and show that its existence depends only on the existence of solutions f…
The Dixmier conjecture and the shape of possible counterexamples II
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
We continue with the investigation began in "The Dixmier conjecture and the shape of possible counterexamples". In that paper we introduced the notion of an irreducible pair (P,Q)…
The Dixmier conjecture and the shape of possible counterexamples
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
We establish a lower bound for the size of possible counterexamples of the Dixmier Conjecture. We prove that , where is the minimum of the greatest common divisor of the…
Non commutative truncated polynomial extensions
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
We introduce the notion of non commutative truncated polynomial extension of an algebra A. We study two families of these extensions. For the first one we obtain a complete classif…
On the centralizers in the Weyl algebra
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
Let P,Q be elements of the Weyl algebra W. We prove that if [Q,P]=1, then the centralizer of P is the polynomial algebra k[P].
Universal deformation formulas and braided module algebras
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
We study formal deformations of a crossed product $S(V)#_f G$, of a polynomial algebra with a group, induced from a universal deformation formula introduced by Witherspoon. These d…
Twisted planes
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
Let k be a commutative ring. We find and characterize a new family of twisted planes (i. e. associative unitary k-algebra structures on the k-module k[X,Y], having k[X] and and k[Y…