Polynomial Identities in Algebras

1. Front Matter

   Pages i-ix

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2. Some Thoughts on the Current State of the Theory of Identical Relations in Lie Algebras

   • Yuri Bahturin

   Pages 1-24

3. Minimal Degree of Identities of Matrix Algebras with Additional Structures

   • Dafne Bessades, Rafael Bezerra dos Santos, Ana Cristina Vieira

   Pages 25-36

4. On the Asymptotics of Capelli Polynomials

   • Francesca Saviella Benanti, Angela Valenti

   Pages 37-56

5. Regev’s Conjecture for Algebras with Hopf Actions

   • Allan Berele

   Pages 57-68

6. ℓ-Weak Identities and Central Polynomials for Matrices

   • Guy Blachar, Eli Matzri, Louis Rowen, Uzi Vishne

   Pages 69-95

7. Computing Multiplicities in the Sign Trace Cocharacters of M _2,1(F)

   • Luisa Carini

   Pages 97-108

8. b-Generalized Skew Derivations on Multilinear Polynomials in Prime Rings

   • Vincenzo De Filippis, Giovanni Scudo, Feng Wei

   Pages 109-138

9. Relatively Free Algebras of Finite Rank

   • Thiago Castilho de Mello, Felipe Yukihide Yasumura

   Pages 139-156

10. Graded Algebras, Algebraic Functions, Planar Trees, and Elliptic Integrals

    • Vesselin Drensky

    Pages 157-194

11. Central Polynomials of Algebras and Their Growth

    • Antonio Giambruno, Mikhail Zaicev

    Pages 195-209

12. Trace Identities on Diagonal Matrix Algebras

    • Antonio Ioppolo, Plamen Koshlukov, Daniela La Mattina

    Pages 211-225

13. Codimension Growth for Weak Polynomial Identities, and Non-integrality of the PI Exponent

    • Plamen Koshlukov, David Levi da Silva Macêdo

    Pages 227-268

14. On Codimensions of Algebras with Involution

    • Daniela La Mattina

    Pages 269-278

15. Context-Free Languages and Associative Algebras with Algebraic Hilbert Series

    • Roberto La Scala, Dmitri Piontkovski

    Pages 279-289

16. On Almost Nilpotent Varieties of Linear Algebras

    • Sergey P. Mishchenko, Angela Valenti

    Pages 291-317

17. (δ, ε)-Differential Identities of UT _m(F)

    • Vincenzo C. Nardozza

    Pages 319-333

18. Identities in Group Rings, Enveloping Algebras and Poisson Algebras

    • Victor Petrogradsky

    Pages 335-354

19. Notes on the History of Identities on Group (and Loop) Algebras

    • C. Polcino Milies

    Pages 355-364

20. Cayley Hamilton Algebras

    • Claudio Procesi

    Pages 365-381

This volume contains the talks given at the INDAM workshop entitled "Polynomial identites in algebras", held in Rome in September 2019. The purpose of the book is to present the current state of the art in the theory of PI-algebras. The review of the classical results in the last few years has pointed out new perspectives for the development of the theory. In particular, the contributions emphasize on the computational and combinatorial aspects of the theory, its connection with invariant theory, representation theory, growth problems. It is addressed to researchers in the field.

• Polynomial Identities
• Free Algebra
• Linear and Multilinear Algebra
• Growth Rate
• Associative Rings and Algebra

• Dipartimento di Matematica, Informatica ed Economia, Università della Basilicata, Potenza, Italy

  Onofrio Mario Di Vincenzo

• Dipartimento di Matematica e Informatica, Università di Palermo, Palermo, Italy

  Antonio Giambruno

Onofrio Mario Di Vincenzo has been a full professor of Algebra since 2000. He currently works at the University of Basilicata where he has been the head of the department for the last 8 years. His research interests focus on the polynomial identities of algebras, in particular in the presence of gradings or involutions acting on them.

Antonio Giambruno received his PhD in Mathematics from the University of Chicago in 1977 under the supervision of Israel N. Herstein. He became a professor at the department of mathematics of the University of Palermo in 1980. He has been a visiting researcher at numerous institutions, including University of Southern California, MSRI, University of Alberta, and University of San Paulo. His research focuses on noncommutative algebra, especially on polynomial identities and their connection with representation theory and asymptotic methods.

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