Related papers: PBW bases for some 3-dimensional skew polynomial a…
In this work we study the automorphisms of skew $PBW$ extensions and skew quantum polynomials. We use Artamonov's works as reference for getting the principal results about automorphisms for generic skew $PBW$ extensions and generic skew…
A Littlewood polynomial is a single-variable polynomial all of whose coefficients lie in $\{ \pm 1\}$. We establish the leading term asymptotics of the number of reciprocal or skew-reciprocal Littlewood polynomials with square discriminant.…
In this paper we define the algebraic sets and the ideal of points for bijective skew PBW extensions with coefficients in left Noetherian domains. Some properties of affine algebraic sets of commutative algebraic geometry will be extended,…
A way to construct and classify the three dimensional polynomially deformed algebras is given and the irreducible representations is presented. for the quadratic algebras 4 different algebras are obtained and for cubic algebras 12 different…
In this paper we discuss for skew $PBW$ extensions the famous Dixmier problem formulated by Jacques Dixmier in 1968. The skew $PBW$ extensions are noncommutative rings of polynomial type and covers several algebras and rings arising in…
The aim of this paper is twofold. The first is to give a quantitative version of Schmidt's subspace theorem for arbitrary families of higher degree polynomials. The second is to give a generalization of the subspace theorem for arbitrary…
In this paper we present a right version of the algorithms developed for to compute Gr\"obner bases over bijective skew PBW extensions in the left case given in [3]. In particular, we adapt the theory of reduction and we build a right…
We consider algebras over a field K defined by a presentation K <x_1,..., x_n : R >, where $R$ consists of n choose 2 square-free relations of the form x_i x_j = x_k x_l with every monomial x_i x_j, i different from j, appearing in one of…
We present an iterative technique to obtain skew-orthogonal polynomials with quartic weight, arising in the study of symplectic ensembles of random matrices.
In the present paper we generalize the notion of a Heyting algebra to the non-commutative setting and hence introduce what we believe to be the proper notion of the implication in skew lattices. We list several examples of skew Heyting…
Scaled Boolean algebras are a category of mathematical objects that arose from attempts to understand why the conventional rules of probability should hold when probabilities are construed, not as frequencies or proportions or the like, but…
We prove that quadratic regular algebras of global dimension three on degree-one generators are related to graded skew Clifford algebras. In particular, we prove that almost all such algebras may be constructed as a twist of either a…
Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…
In this paper we present a first approach toward a \texttt{SAGBI} bases theory of skew Poincar\'e-Birkhoff-Witt extensions, and investigate the problem of polynomial composition for \texttt{SAGBI} bases of subalgebras of these extensions.
The purposes of this article are threefold. First, to determine numerically when an arbitrary blowup of a smooth surface is smooth. We show the surface is smooth if and only if certain rational parameters involving log discrepancy and…
We construct a linear basis of a free GDN superalgebra over a field of characteristic $\neq 2$. As applications, we prove a PBW theorem, that is, any GDN superalgebra can be embedded into its universal enveloping commutative associative…
We prove that if $A$ is a regular graded skew Clifford algebra and is a twist of a regular graded Clifford algebra $B$ by an automorphism, then the subalgebra of $A$ generated by a certain normalizing sequence of homogeneous degree-two…
We establish necessary or sufficient conditions to guarantee that skew Poincar\'e-Birkhoff-Witt extensions are NI or NJ rings. Our results extend those corresponding for skew polynomial rings and establish similar properties for other…
Let $S$ be a domain and $R=S[t;\sigma,\delta]$ a skew polynomial ring, where $\sigma$ is an injective endomorphism of $S$ and $\delta$ a left $\sigma$ -derivation. We give criteria for skew polynomials $f\in R$ of degree less or equal to…
In this short paper we study for the skew PBW (Poincar\'e-Birkhoff-Witt) extensions some homological properties arising in non-commutative algebraic geometry, namely, Auslander-Gorenstein regularity, Cohen-Macaulayness and strongly…