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We compute the graded polynomial identities for the variety of graded algebras generated by the Lie algebra of upper triangular matrices of order 3 over an arbitrary field and endowed with an elementary grading. We investigate the Specht property for
Externí odkaz:
http://arxiv.org/abs/2412.13325
Autor:
Zimmermann, Alexander
We define and characterise completely dg-separable dg-extensions $\varphi:(A,d_A)\rightarrow (B,d_B)$. We completely characterise the case of graded commutative dg-division algebras in characteristic different from $2$. We prove that for a dg-separab
Externí odkaz:
http://arxiv.org/abs/2412.06526
Autor:
Karimjanov, I. A.
In the present paper, we give the classification of a subclass of n-dimensional naturally graded associative algebras with nilindex $n-3$. The subclass has the characteristic sequence $C(\mathcal{A})=(n-3,2,1)$. The result completes the classificatio
Externí odkaz:
http://arxiv.org/abs/2412.04817
Autor:
Karimjanov, I. A.
In the paper, we describe $n$-dimensional naturally graded nilpotent associative algebras with the characteristic sequence $C(\mathcal{A})=(n-p,1,\dots,1)$ as called $p-$filiform algebras over the field of the complex numbers.
Externí odkaz:
http://arxiv.org/abs/2412.03964
Autor:
Dramburg, Darius, Sandøy, Mads Hustad
We investigate compatibility of gradings for an almost Koszul or Koszul algebra $R$ that is also the higher preprojective algebra $\Pi_{n+1}(A)$ of an $n$-hereditary algebra $A$. For an $n$-representation finite algebra $A$, we show that $A$ must be
Externí odkaz:
http://arxiv.org/abs/2411.13283
Let $K \langle X\rangle$ be the free associative algebra freely generated over the field $K$ by the countable set $X = \{x_1, x_2, \ldots\}$. If $A$ is an associative $K$-algebra, we say that a polynomial $f(x_1,\ldots, x_n) \in K \langle X\rangle$ i
Externí odkaz:
http://arxiv.org/abs/2411.06964
Autor:
Gaddis, Jason, Oswald, Amrei
We classify actions of generalized Taft algebras on preprojective algebras of extended Dynkin quivers of type $A$. This may be viewed as an extension of the problem of classifying actions on the polynomial ring in two variables. In cases where the gr
Externí odkaz:
http://arxiv.org/abs/2410.24179
Autor:
de França, Antonio
Let $\mathbb{F}$ be a field and $\mathsf{G}$ a group. This work is inspired in the following problem: "{\it given a division (simple) $\mathsf{G}$-graded $\mathbb{F}$-algebra, is there any other division (simple) $\mathsf{G}$-graded $\mathbb{F}$-alge
Externí odkaz:
http://arxiv.org/abs/2410.13183
Autor:
Rubiano, Andrés, Reyes, Armando
In this paper, we study the differential smoothness of diffusion algebras.
Comment: 32 pages. arXiv admin note: text overlap with arXiv:2409.18947, arXiv:2408.16648, arXiv:2409.10264
Comment: 32 pages. arXiv admin note: text overlap with arXiv:2409.18947, arXiv:2408.16648, arXiv:2409.10264
Externí odkaz:
http://arxiv.org/abs/2410.12701
Let $G$ be a group coacting on an Artin-Schelter regular algebra $A$ homogeneously and inner-faithfully. When the identity component $A_e$ is also Artin-Schelter regular, providing a generalization of the Shephard-Todd-Chevalley Theorem, we say that
Externí odkaz:
http://arxiv.org/abs/2410.08959