Polynomial identities and their numerical invariants

Author(s)

Kauê Orlando Pereira

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2023-02-28

Examining board members

Plamen Emilov Kochloukov; Thiago Castilho de Mello; Antonio Ioppolo

• Advisor: Plamen Emilov Kochloukov

Abstract

The main goal of this dissertation is to show several characterizations of varieties with polynomial growth in their codimensions, following the works of Kemer, Giambruno and Zaicev. In order to achieve this goal, it was necessary to develop a theoretical background on the theory of the PI exponent. In this work we prove the famous theorem due Giambruno and Zaicev about the existence of the PI exponent, and to this end it was necessary to have the foundation of the works of Kemer on superalgebras and the Grassmann Envelope, as well as the theory of representations of the symmetric group S_n (AU)

• FAPESP's process: 20/16595-7 - Polynomial identities and their numerical invariants
• Grantee: Kauê Orlando Pereira
• Support Opportunities: Scholarships in Brazil - Master