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EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

Part of: Hopf algebras, quantum groups and related topics Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  01 December 2020

NICOLÁS ANDRUSKIEWITSCH ,
DIRCEU BAGIO ,
SARADIA DELLA FLORA  and
DAIANA FLÔRES
NICOLÁS ANDRUSKIEWITSCH
Affiliation:
FAMAF-Universidad Nacional de Córdoba, CIEM (CONICET), Medina Allende s/n, Ciudad Universitaria, (5000) Córdoba, República Argentina e-mail: [email protected]
DIRCEU BAGIO
Affiliation:
Departamento de Matemática, Universidade Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil e-mails: [email protected]; [email protected]; [email protected]
SARADIA DELLA FLORA
Affiliation:
Departamento de Matemática, Universidade Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil e-mails: [email protected]; [email protected]; [email protected]
DAIANA FLÔRES
Affiliation:
Departamento de Matemática, Universidade Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil e-mails: [email protected]; [email protected]; [email protected]
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Abstract

We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

MSC classification

Primary: 16T20: Ring-theoretic aspects of quantum groups
Secondary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 1 , January 2022 , pp. 65 - 78
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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Footnotes

†

This material is based upon work supported by the National Science Foundation under Grant No. DMS-1440140, while N. A. was in residence at the Mathematical Sciences Research Institute in Berkeley, California, in the Spring 2020 semester. The work of N. A. was partially supported by CONICET, Secyt (UNC), and the Alexander von Humboldt Foundation through the Research Group Linkage Programme.

References

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