Related papers: Differential smoothness of bi-quadratic algebras w…

In this paper, we investigate the differential smoothness of bi-quadratic algebras on three generators with PBW basis.

The aim of the paper is to give an explicit description of bi-quadratic algebras on 3 generators with PBW basis.

In this paper, we investigate the differential smoothness of skew PBW extensions over commutative polynomial rings on one and two indeterminates.

In this paper, we study the differential smoothness of 3-dimensional skew polynomial algebras and diffusion algebras.

We investigate the differential smoothness of a certain family of skew Poincar\'e-Birkhoff-Witt extensions.

In this paper, we study the differential smoothness of diffusion algebras.

In this paper, we investigate the differential smoothness of graded skew Clifford algebras.

It is shown that, under some natural assumptions, the tensor product of differentially smooth algebras and the skew-polynomial rings over differentially smooth algebras are differentially smooth.

We construct an integral PBW basis and an integral crystal basis of the quantum affine algebra of type A$_{2}^{(2)}$.

We classify PBW-deformations of quadratic-constant type of certain quantizations of exterior algebras. These correspond to the fundamental modules of quantum $\mathfrak{sl}_N$, their duals, and their direct sums. We show that the first two…

The simplest version of the Spin-polynomial invariants of the underlying differentiable structures of algebraic surfaces were considered and the simplest arguments were used in order to distinguish the underlying smooth structures of…

This paper proposes a new notion of smoothness of algebras, termed differential smoothness, that combines the existence of a top form in a differential calculus over an algebra together with a strong version of the Poincar\'e duality…

This note has two purposes. First we establish that the map defined in [L, $\S 40.2.5$ (a)] is an isomorphism for certain admissible sequences. Second we show the map gives rise to a convex basis of Poincar\'e--Birkhoff--Witt (PBW) type for…

The aim of this paper is to establish necessary and sufficient algorithmic conditions to guarantee that an algebra is actually a 3-dimensional skew polynomial algebra in the sense of Bell and Smith.

We determine endomorphism algebras of abelian surfaces with quaternion multiplication.

In recent years, various nonlinear algebraic structures have been obtained in the context of quantum systems as symmetry algebras, Painlev\'{e} transcendent models and missing label problems. In this paper we treat all of these algebras as…

In this paper we discuss a generalization of the classica PBW-theorem to the case of Koszul algebras. Our result is a slight generalization of that obtained by A.Polischuk and L.Positselsky, but the proof is different and uses deformation…

We determine sufficient criteria for the differential smoothness of ambiskew polynomial rings defined and studied by D. A. Jordan in several papers \cite{FishJordan2019, Jordan1993b, Jordan2000, JordanWells2013}.

For a quotient algebra $U$ of the tensor algebra we give explicit conditions on its relations for $U$ being a PBW-deformation of an $N$-Koszul algebra $A$. We show there is a one-one correspondence between such deformations and a class of…

We solve the PBW-like problem of normal ordering for enveloping algebras of direct sums.