Work

The 2 × 2 upper triangular matrix algebra and its generalized polynomial identities

Year: 2024

Type: article

Abstract: Let U T 2 be the algebra of 2 × 2 upper triangular matrices over a field F of characteristic zero. Here we study the generalized polynomial identities of U T 2 , i.e., identical relations holding for U T 2 regarded as U T 2 -algebra. We determine the generator of the T U T 2 -ideal of generalized polynomial identities of U T 2 and compute the exact values of the corresponding sequence of generalized codimensions. Moreover, we give a complete description of the space of multilinear generalized identities in n variables in the language of Young diagrams through the representation theory of the symmetric group S n . Finally, we prove that, unlike the ordinary case, the generalized variety of U T 2 -algebras generated by U T 2 has no almost polynomial growth; nevertheless, we exhibit two distinct generalized varieties of almost polynomial growth.

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2024.12.005

Authors: Fabrizio Martino, Carla Rizzo

Institutions: University of Palermo, Centro de Matemática, University of Coimbra

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,140