Communications in Mathematics

Communications in Mathem. ONL

<abstract>
<title style='display:none'>Abstract</title>
In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.
</abstract>

Abstract

Keywords

MSC 2010

<article-title>Existentially closed Leibniz algebras and an embedding theorem</article-title>

Existentially closed Leibniz algebras and an embedding theorem

{"article-title":"Existentially closed Leibniz algebras and an embedding theorem"}

<abstract>
<title style='display:none'>Abstract</title>
A rook placement is a subset of a root system consisting of positive roots with pairwise non-positive inner products. To each rook placement in a root system one can assign the coadjoint orbit of the Borel subgroup of a reductive algebraic group with this root system. Degenerations of such orbits induce a natural partial order on the set of rook placements. We study combinatorial structure of the set of rook placements in <italic>An−</italic>1 with respect to a slightly different order and prove that this poset is graded.
</abstract>

<article-title>Gradedness of the set of rook placements in <italic>A</italic><italic>n</italic>−1</article-title>

Gradedness of the set of rook placements in 

<abstract>
<title style='display:none'>Abstract</title>
We describe the images of multilinear polynomials of arbitrary degree evaluated on the 3×3 upper triangular matrix algebra over an infinite field.
</abstract>

<article-title>The image of multilinear polynomials evaluated on 3 × 3 upper triangular matrices</article-title>

The image of multilinear polynomials evaluated on 3 × 3 upper triangular matrices

<abstract>
<title style='display:none'>Abstract</title>
In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We describe the pre-derivations of filiform Leibniz algebras for the first and second families and determine those algebras in the first two classes of filiform Leibniz algebras that are non-strongly nilpotent.
</abstract>

Department of Mathematics, Institute of Mathematics, Campus Vida

<article-title>Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras</article-title>

Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras

<abstract>
<title style='display:none'>Abstract</title>
In this article, we provide an algorithm with Wolfram Mathematica code that gives a unified computational power in classification of finite dimensional nilpotent algebras using Skjelbred-Sund method. To illustrate the code, we obtain new finite dimensional Moufang algebras.
</abstract>

<article-title>Unified computational approach to nilpotent algebra classification problems</article-title>

Unified computational approach to nilpotent algebra classification problems

{"article-title":"Unified computational approach to nilpotent algebra classification problems"}

<abstract>
<title style='display:none'>Abstract</title>
We give the description of Rota–Baxter operators, Reynolds operators, Nijenhuis operators and average operators on 3-dimensional nilpotent associative algebras over ℂ.
</abstract>

<article-title>Rota-type operators on 3-dimensional nilpotent associative algebras</article-title>

Rota-type operators on 3-dimensional nilpotent associative algebras

{"article-title":"Rota-type operators on 3-dimensional nilpotent associative algebras"}

<abstract>
<title style='display:none'>Abstract</title>
Let (𝔘, <italic>ɛu</italic>) and (𝔅, <italic>ɛb</italic>) be two pointed sets. Given a family of three maps <italic>ℱ</italic> = {<italic>f</italic>1 : 𝔘 → 𝔘; <italic>f</italic>2 : 𝔘 × 𝔘 <italic>→</italic> 𝔘; <italic>f</italic>3 : 𝔘 × 𝔘 <italic>→</italic> 𝔅}, this family provides an adequate decomposition of 𝔘 \ {<italic>ɛu</italic>} as the orthogonal disjoint union of well-described <italic>ℱ</italic>-invariant subsets. This decomposition is applied to the structure theory of graded involutive algebras, graded quadratic algebras and graded weak <italic>H</italic>*-algebras.
</abstract>

Department of Mathematics, Faculty of Sciences

<article-title>Certain partitions on a set and their applications to different classes of graded algebras</article-title>

Certain partitions on a set and their applications to different classes of graded algebras

<abstract>
<title style='display:none'>Abstract</title>
In the present paper we prove that every local and 2-local derivation on conservative algebras of 2-dimensional algebras are derivations. Also, we prove that every local and 2-local automorphism on conservative algebras of 2-dimensional algebras are automorphisms.
</abstract>

<article-title>Conservative algebras of 2-dimensional algebras, III</article-title>

Conservative algebras of 2-dimensional algebras, III

{"article-title":"Conservative algebras of 2-dimensional algebras, III"}

<abstract>
<title style='display:none'>Abstract</title>
We connect the theorems of <xref ref-type="bibr" rid="j_cm-2021-0024_ref_018">Rentschler [18]</xref> and <xref ref-type="bibr" rid="j_cm-2021-0024_ref_010">Dixmier [10]</xref> on locally nilpotent derivations and automorphisms of the polynomial ring <italic>A</italic>0 and of the Weyl algebra <italic>A</italic>1, both over a field of characteristic zero, by establishing the same type of results for the family of algebras 
<disp-formula id="j_cm-2021-0024_eq_001">
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_cm-2021-0024_eq_001.png"/>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>〈</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>|</mml:mo><mml:mi>y</mml:mi><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:mi>x</mml:mi><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>〉</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math>
<tex-math>{A_h} = \left\langle {x,y|yx - xy = h\left( x \right)} \right\rangle ,</tex-math>
</alternatives>
</disp-formula>
, where <italic>h</italic> is an arbitrary polynomial in <italic>x</italic>. In the second part of the paper we consider a field 𝔽 of prime characteristic and study 𝔽[<italic>t</italic>]-comodule algebra structures on <italic>Ah</italic>. We also compute the Makar-Limanov invariant of absolute constants of <italic>Ah</italic> over a field of arbitrary characteristic and show how this subalgebra determines the automorphism group of <italic>Ah</italic>.
</abstract>

CMUP, Departamento de Matemática, Faculdade de Ciências

<article-title>Actions of the additive group <italic>Ga</italic> on certain noncommutative deformations of the plane</article-title>

Actions of the additive group  on certain noncommutative deformations of the plane

<abstract>
<title style='display:none'>Abstract</title>
We find examples of polynomials <italic>f</italic> ∈ <italic>D</italic> [<italic>t</italic>; <italic>σ, δ</italic>] whose eigenring <italic>ℰ</italic>(<italic>f</italic>) is a central simple algebra over the field <italic>F</italic> = <italic>C</italic> ∩ Fix(<italic>σ</italic>) ∩ Const(<italic>δ</italic>).
</abstract>

<article-title>A generalisation of Amitsur’s A-polynomials</article-title>

A generalisation of Amitsur’s A-polynomials

{"article-title":"A generalisation of Amitsur\u2019s A-polynomials"}

<abstract>
<title style='display:none'>Abstract</title>
Let <italic>R</italic> be an associative algebra over a field <italic>K</italic> generated by a vector subspace <italic>V</italic>. The polynomial <italic>f</italic>(<italic>x</italic>1, . . . , <italic>xn</italic>) of the free associative algebra <italic>K</italic>〈<italic>x</italic>1, <italic>x</italic>2, . . .〉 is a weak polynomial identity for the pair (<italic>R, V</italic>) if it vanishes in <italic>R</italic> when evaluated on <italic>V</italic>. We survey results on weak polynomial identities and on their applications to polynomial identities and central polynomials of associative and close to them nonassociative algebras and on the finite basis problem. We also present results on weak polynomial identities of degree three.
</abstract>

<article-title>Weak polynomial identities and their applications</article-title>

Weak polynomial identities and their applications

{"article-title":"Weak polynomial identities and their applications"}

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Communications in Mathematics ist in den folgenden Services indiziert: <ul> <li> Baidu Scholar </li> <li> Cabell's Whitelist </li> <li> CNKI Scholar (China National Knowledge Infrastructure) </li> <li> CNPIEC - cnpLINKer </li> <li> Dimensions </li> <li> DOAJ (Directory of Open Access Journals) </li> <li> EBSCO (relevant databases) </li> <li> EBSCO Discovery Service </li> <li> GoOA </li> <li> Google Scholar </li> <li> Japan Science and Technology Agency (JST) </li> <li> J-Gate </li> <li> JournalGuide </li> <li> JournalTOCs </li> <li> KESLI-NDSL (Korean National Discovery for Science Leaders) </li> <li> Mathematical Reviews (MathSciNet) </li> <li> Microsoft Academic </li> <li> MyScienceWork </li> <li> Naver Academic </li> <li> Naviga (Softweco) </li> <li> Primo Central (ExLibris) </li> <li> Publons </li> <li> QOAM (Quality Open Access Market) </li> <li> ReadCube </li> <li> SCImago (SJR) </li> <li> SCOPUS </li> <li> Semantic Scholar </li> <li> Summon (ProQuest) </li> <li> TDNet </li> <li> Ulrich's Periodicals Directory/ulrichsweb </li> <li> WanFang Data </li> <li> WorldCat (OCLC) </li> <li> Zentralblatt Math (zbMATH) </li> </ul>

Editor-in-Chief Pasha Zusmanovich Department of Mathematics, Faculty of Science, University of Ostrava, 30 April 22, 701 03 Ostrava 1, Czech Republic 　 　 Editors Ilka Agricola FB 12, Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Str., Campus Lahnberge, 35032 Marburg, Germany 　 Diana Barseghyan, University of Ostrava, Czech Republic Attila Bérczes Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary Yuri Bilu, University of Bordeaux, France Anthony Bloch Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109-1043, USA 　 　 Karl Dilcher Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada 　 Alberto Elduque, University of Zaragoza, Spain Giuseppe Gaeta Università degli Studi di Milano, Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy Yong-Xin Guo Eastern Liaoning University, No. 116 Linjiang Back Street, Zhen’an District, Dandong, Liaoning, 118001, China Ari Laptev Department of Mathematics, Imperial College London, Huxley Building, 180 Queen's Gate, London SW7 2AZ, UK Institut Mittag-Leffler, Auravägen 17, 182 60 Djursholm, Sweden Dimitry Leites, Stockholm University; New York University Abu Dhabi　 Haizhong Li Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China Valentin Lychagin Department of Mathematics and Statistics, Faculty of Science and Technology, UiT The Arctic University of Norway, N-9037 Tromsø, Norway &amp; V. A. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, Russia, 117997, Moscow, Profsoyuznaya st., 65 Sophie Morier-Genoud, Sorbonne Université, France Valentin Ovsienko, University of Reims and CNRS, France Dmitrii Pasechnik, University of Oxford, United Kingdom Geoff Prince Department of Mathematics and Statistics, La Trobe University Melbourne, Victoria 3086, Australia Olga Rossi Department of Mathematics, Faculty of Science, The University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic and Department of Mathematics and Statistics, La Trobe University Melbourne, Victoria 3086, Australia Eric Swartz Department of Mathematics, College of William &amp; Mary, P.O. Box 8795, Williamsburg, VA, 23187-8795, USA Francesco Toppan,Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brasil Nikolay Vavilov, St. Petersburg State University, Russia Thomas Vetterlein Department of Knowledge-Based Mathematical Systems, Faculty of Engineering and Natural Sciences, Johannes Kepler University Linz, Altenberger Straße 69, 4040 Linz, Austria Sebastian Walcher RWTH Aachen, Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen, Germany Sergei Yakovenko, Weizmann Institute, Rehovot Previous Editors George Bluman (Vancouver, 2010–2017) Stephen Glasby (Perth, 2010-2017) Vilém Novák (Ostrava, 2010-2018) Štefan Porubský (Prague, 2010–2013) †Gennadi Sardanashvily (Moscow, 2015–2016) Technical Editors Lukáš Novotný Department of Mathematics, Faculty of Science, The University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic 　 Jan Šustek Department of Mathematics, Faculty of Science, The University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic Contact <A href="mailto:cm@osu.cz">cm@osu.cz</A> Publisher De Gruyter Poland Bogumiła Zuga 32A Str. 01-811 Warsaw, Poland T: +48 22 701 50 15

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<DIV align=left> Communications in Mathematics publishes original research papers and survey papers in pure and applied mathematics. To be acceptable for publication, the paper must be significant, original and correct. High quality review papers of interest to a wide range of scientists in mathematics and its applications are equally welcome. The journal does not have article processing charges (APCs) nor article submission charges. Why submit <UL> <LI>Constructive peer review </LI> <LI>Constructive single-blind peer review </LI> <LI>Distinguished editorial board ensuring high quality </LI> <LI>No page charges </LI> <LI>Easy electronic submission and tracking the article's progress online </LI> <LI>Rapid publication - online within 2 months of acceptance of final version </LI> <LI>The corresponding author receives the pdf file of the published article </LI> <LI>Full-text access FREE to readers </LI> <LI>FREE use of colour and multimedia in the online edition </LI></UL> Archiving Sciendo archives the contents of this journal in <A href="https://www.portico.org/">Portico</A> - digital long-term preservation service of scholarly books, journals and collections. Plagiarism Policy The editorial board is participating in a growing community of <A href="https://www.crossref.org/services/similarity-check/">Similarity Check System's</A> users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. Target Group: <UL> <LI>researchers in all areas of pure and applied mathematics </LI></UL></DIV>

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Volumen 29 (2021): Heft 2 (June 2021)
Special Heft: 3rd International Workshop on Nonassociative Algebras in Málaga