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1. Differential Identities and Polynomial Growth of the Codimensions

   Let A be an associative algebra over a field F of characteristic zero and let L be a Lie algebra over F . If L acts on A by derivations, then such an...

   Carla Rizzo, Rafael Bezerra dos Santos, Ana Cristina Vieira in Algebras and Representation Theory

   Article 05 September 2022

2. Varieties of Group Graded Algebras with Graded Involution of Almost Polynomial Growth

   Classifications of varieties of algebras of almost polynomial growth were considered by several authors in different contexts. An algebra graded by a...

   L. M. C. Oliveira, R. B. dos Santos, A. C. Vieira in Algebras and Representation Theory

   Article 30 November 2021

3. Varieties of Null-Filiform Leibniz Algebras Under the Action of Hopf Algebras

   Let L be an n -dimensional null-filiform Leibniz algebra over a field K . We consider a finite dimensional cocommutative Hopf algebra or a Taft algebra H ...

   Lucio Centrone, Chia Zargeh in Algebras and Representation Theory

   Article Open access 20 October 2021

4. A Characterization of Superalgebras with Pseudoinvolution of Exponent 2

   Let A be a superalgebra endowed with a pseudoinvolution ∗ over an algebraically closed field of characteristic zero. If A satisfies an ordinary...

   Antonio Ioppolo in Algebras and Representation Theory

   Article 22 September 2020

5. Diophantine quadruples with the properties \(D(n_1)\) and \(D(n_2)\)

   Andrej Dujella, Vinko Petričević in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

   Article 07 December 2019

6. Classifying Algebras with Graded Involutions or Superinvolutions with Multiplicities of their Cocharacter Bounded by One

   Let A be superalgebra over a field of characteristic zero and let ∗ be either a graded involution or a superinvolution defined on A . In this paper we...

   Fabrizio Martino in Algebras and Representation Theory

   Article 22 January 2020

7. Graded Identities of Several Tensor Products of the Grassmann Algebra

   Let F be an infinite field of characteristic different from two and E be the unitary Grassmann algebra of an infinite dimensional F -vector space L ....

   Lucio Centrone, Viviane Ribeiro Tomaz da Silva in Algebras and Representation Theory

   Article 30 September 2020

8. Graded Identities and Central Polynomials for the Verbally Prime Algebras

   Let F be a field of characteristic zero and let R be an algebra that admits a regular grading by an abelian group H . Moreover, we consider G a group...

   Claudemir Fidelis, Diogo Diniz, ... Plamen Koshlukov in Algebras and Representation Theory

   Article 30 July 2021

9. The Grassmann Algebra and its Differential Identities

   Let G be the infinite dimensional Grassmann algebra over an infinite field F of characteristic different from two. In this paper we study the...

   Carla Rizzo in Algebras and Representation Theory

   Article 23 November 2018

10. Non integral exponential growth of central polynomials

    Antonio Giambruno, Sergey Mishchenko, Mikhail Zaicev in Archiv der Mathematik

    Article 12 October 2018

11. Superalgebras with Involution or Superinvolution and Almost Polynomial Growth of the Codimensions

    Antonio Giambruno, Antonio Ioppolo, Daniela La Mattina in Algebras and Representation Theory

    Article 07 June 2018

12. A-identities for the \({2 \times 2}\) matrix algebra

    Dimas José Gonçalves, Waldeck Schützer, Humberto Luiz Talpo in Archiv der Mathematik

    Article 12 March 2016

13. Varieties of Algebras with Superinvolution of Almost Polynomial Growth

    Antonio Giambruno, Antonio Ioppolo, Daniela La Mattina in Algebras and Representation Theory

    Article 28 December 2015

14. Asymptotics for Graded Capelli Polynomials

    The finite dimensional simple superalgebras play an important role in the theory of PI-algebras in characteristic zero. The main goal of this paper...

    Francesca Benanti in Algebras and Representation Theory

    Article 16 July 2014

15. Zariski Closed Algebras in Varieties of Universal Algebra

    The Zariski closure of an arbitrary representable (not necessarily associative) algebra is studied in the general context of universal algebra, with...

    Alexei Belov-Kanel, Antonio Giambruno, ... Uzi Vishne in Algebras and Representation Theory

    Article 18 March 2014

16. Graded Identities of Some Simple Lie Superalgebras

    We study ℤ ₂ -graded identities of Lie superalgebras of the type b ( t ), t  ≥ 2, over a field of characteristic zero. Our main result is that the n -th...

    Dušan Repovš, Mikhail Zaicev in Algebras and Representation Theory

    Article 24 October 2013

17. Derivations, Gradings, Actions of Algebraic Groups, and Codimension Growth of Polynomial Identities

    A. S. Gordienko, M. V. Kochetov in Algebras and Representation Theory

    Article 13 March 2013

18. ∗-Polynomial Identities of a Nonsymmetric ∗-Minimal Algebra

    Let F be an infinite field of characteristic ≠ 2. We study the ∗-polynomial identities of the ∗-minimal algebra R  =  UT _∗ ( F  ⊕  F , F ). We describe the...

    Onofrio M. Di Vincenzo, Vincenzo Nardozza in Algebras and Representation Theory

    Article 22 November 2012

19. Cocharacters of Bilinear Map**s and Graded Matrices

    Let M _k ( F ) be the algebra of k × k matrices over a field F of characteristic 0. If G is any group, we endow M _k ( F ) with the elementary grading...

    Stefania Aquè, Antonio Giambruno in Algebras and Representation Theory

    Article 07 September 2012

20. The Gelfand–Kirillov dimension of the universal algebras of M _a,b (E)⊗E in positive characteristic

    In this paper we calculate the Gelfand–Kirillov dimension of the relatively free (also called universal) algebra of rank m , U _m ( M _{a , b ...}

    Sérgio M. Alves, Fernanda G. de Paula, Marcello Fidelis in Rendiconti del Circolo Matematico di Palermo

    Article 16 November 2011