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pro vyhledávání: '"Lopes, Samuel A."'
Working over an arbitrary field of characteristic different from $2$, we extend the Skjelbred-Sund method to compatible Lie algebras and give a full classification of nilpotent compatible Lie algebras up to dimension $4$. In case the base field is cu
Externí odkaz:
http://arxiv.org/abs/2406.04036
Publikováno v:
Linear Mult. Alg. 71 (2023), no. 12, 1994-2007
We consider a Leibniz algebra ${\mathfrak L} = {\mathfrak I} \oplus {\mathfrak V}$ over an arbitrary base field $\mathbb{F}$, being ${\mathfrak I}$ the ideal generated by the products $[x,x], x \in {\mathfrak L}$. This ideal has a fundamental role in
Externí odkaz:
http://arxiv.org/abs/2401.13018
In this paper, we study the category of modules over the Smith algebra which are free of finite rank over the unital polynomial subalgebra generated by the Cartan element $h$ and obtain families of such simple modules of arbitrary rank. In the case o
Externí odkaz:
http://arxiv.org/abs/2308.07881
Autor:
Lopes, Samuel A.
Publikováno v:
Communications in Mathematics, Volume 32 (2024), Issue 3 (Special issue: Portuguese Mathematics) (December 21, 2023) cm:11678
This is an abridged version of our Habilitation thesis. In these notes, we aim to summarize our research interests and achievements as well as motivate what drives our work: symmetry, structure and invariants. The paradigmatic example which permeates
Externí odkaz:
http://arxiv.org/abs/2307.16808
This paper extends an algorithm and canonical embedding by Cauchon to a large class of quantum algebras. It applies to iterated Ore extensions over a field satisfying some suitable assumptions which cover those of Cauchon's original setting but also
Externí odkaz:
http://arxiv.org/abs/2304.02151
Publikováno v:
In Journal of Algebra 1 October 2024 655:405-423
Autor:
Devos, Rafaela Julyana Barboza, Bender, Letícia Eduarda, Lopes, Samuel Teixeira, Cavanhi, Vítor Augusto Farina, Colvero, Gabriel Lanza, Rempel, Alan, Harakava, Ricardo, Alves, Sérgio Luiz, Jr, Colla, Luciane Maria
Publikováno v:
In Process Biochemistry June 2024 141:90-101
We give a geometric classification of $n$-dimensional nilpotent, commutative nilpotent and anticommutative nilpotent algebras. We prove that the corresponding geometric varieties are irreducible, find their dimensions and describe explicit generic fa
Externí odkaz:
http://arxiv.org/abs/2102.10392
We give the complete algebraic classification of all complex 4-dimensional nilpotent algebras. The final list has 234 (parametric families of) isomorphism classes of algebras, 66 of which are new in the literature.
Comment: arXiv admin note: tex
Comment: arXiv admin note: tex
Externí odkaz:
http://arxiv.org/abs/2012.00525
Autor:
Lopes, Samuel A., Razavinia, Farrokh
In [14] we introduced a new class of algebras, which we named \textit{quantum generalized Heisenberg algebras} and which depend on a parameter $q$ and two polynomials $f,g$. We have shown that this class includes all generalized Heisenberg algebras (
Externí odkaz:
http://arxiv.org/abs/2009.05270