环与代数

This paper introduces and studies a class of Weyl-type algebras \(A_{p,t,\cA} = \Weyl{e^{\pm x^{p} e^{t x}},\; e^{\cA x},\; x^{\cA}}\) constructed over exponential-polynomial rings, where \(\FF\) is a field of characteristic zero, \(\cA\)…

Let $\mathfrak{g}$ be a Color Lie Algebra and $\mathcal{U}(\mathfrak{g})$ its the universal Enveloping Algebra. We define the notion of graded deformations and we give explicit graded deformations of the universal Enveloping Algebra of…

In recent years, many results have been established regarding classifications of varieties whose colength sequences are bounded by a fixed constant. In this work, we explore this theme in the setting of algebras endowed with a graded…

Subalgebras of upper triangular matrix algebras have played a fundamental role in the classification of minimal varieties of polynomial growth. Such classification has become a source of study in recent years since it leads to the more…

We prove that two finite prime $\Omega$-algebras defined over the same unital commutative ring and satisfying the same set of polynomial identities are isomorphic.

In quantum mechanics, associative algebras play an important role in understanding symmetries and operator algebras, providing new algebraic frameworks for describing physical systems. This work classifies associative algebras over a field…

We examine the Hochschild cohomology for triangular algebras that capture some aspects of geometry and topology of the torus and of the quadric surface, and for deformations of these algebras. In particular, this shows that the cup product…

Tight and essentially tight modules generalize weakly injective modules. Essential tightness requires embeddings to be essential. This restriction makes the two notions totally different. In this note, we investigate cases when those two…

Dotsenko and Vallette discovered an extension to nonsymmetric operads of Buchberger's algorithm for Gr\"obner bases of polynomial ideals. In the free nonsymmetric operad with one ternary operation $({\ast}{\ast}{\ast})$, we compute a…

DNA recombination is a fundamental biological process that encodes genetic information for organism development and function. In this study, we construct the left symmetric algebras arising from the operation of DNA insertion. We define a…

Let $Z(\cal L)$ be the center of a Lie algebra $\cal L$ with Lie bracket $[\cdot, \cdot]$. %We then define The commuting graph of $\cal L$ is then defined by the simple undirected graph $\Gamma({\cal L})=(V_{\cal L},E_{\cal L})$ in which…

Let $B = \Bbbk_q[u,v]^{C_{n+1}}$ be a Type $\mathbb{A}_n$ quantum Kleinian singularity, which is an example of a noncommutative surface singularity. This singularity is known to have a noncommutative quasi-crepant resolution $\Lambda$,…

An important aspect in the theory of algebras with polynomial identities is the study of the asymptotic behavior of the codimension sequence $c_n(A),\, n\geq 1,$ which measures the growth of polynomial identities of a given algebra $A$. In…

This paper investigates the Jordan--Kronecker invariant of finite dimensional complex Lie algebras. We present an explicit algorithm for determining the type of a given Lie algebra from its Jordan--Kronecker invariant. The algorithm is…

We classify all homogeneous odd (i.e., parity-reversing) Rota--Baxter operators of weight zero on the modified Witt-type Lie superalgebra $W = \langle L_m, G_n \rangle_{m,n\in\Z}$. Our classification shows that nontrivial such operators are…

We present the first classification of algebraic identities in 3 variables for linear operators on associative structures. We work in the context of associative triple systems, but since any associative algebra with product $xy$ becomes an…

The purpose of this paper is to prove the First and Second Fundamental Theorems of invariant theory for the complex special linear supergroup and discuss the superalgebra of invariants, via the super Plucker relations.

In previous papers, the author showed that in many cases of interest there exists an isomorphism between certain path algebras related to the structure of the subregular J-rings of Coxeter systems and matrix rings over a free product of…

We study well-rounded ideal lattices from totally definite quaternion algebras. We prove existence and classification results, and illustrate our methods with examples.

We investigate a class of algebras on $\mathbb{R}^3$ arising and generalized from the algebraic structure of magnetic gradient fields induced by systems of synchronous magnets with identical dipole moments (i.e.,…