Arkiv för Matematik

Volume 60 (2022)

Number 2

On the double of the Jordan plane

Pages: 213 – 229

DOI: https://dx.doi.org/10.4310/ARKIV.2022.v60.n2.a1

Authors

Nicolás Andruskiewitsch (Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, CIEM-CONICET, Medina Allende s/n (5000) Ciudad Universitaria, Córdoba, Argentina)

François Dumas (LMBP, Université Clermont Auvergne, CNRS, Clermont-Ferrand, France)

Héctor Martín Peña Pollastri (Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, CIEM-CONICET, Medina Allende s/n (5000) Ciudad Universitaria, Córdoba, Argentina)

Abstract

We compute the simple finite-dimensional modules and the center of the Drinfeld double of the Jordan plane introduced in [Andruskiewitsch, N. and Peña Pollastri, H. M., “On the restricted Jordan plane in odd characteristic”, J. Algebra Appl. 20, 2140012 (2021). MR4209966] assuming that the characteristic is zero.

Keywords

Drinfeld double, Jordan plane, Nichols algebra, Weyl algebra

2010 Mathematics Subject Classification

Primary 16T05. Secondary 16S36, 16T20.

Full Text (PDF format)

Received 3 September 2021

Received revised 25 January 2022

Accepted 4 February 2022

Published 26 October 2022