Nichols algebras with standard braiding

Angiono, Iván

doi:10.2140/ant.2009.3.35

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Nichols algebras with standard braiding

Iván Ezequiel Angiono

Vol. 3 (2009), No. 1, 35–106

DOI: 10.2140/ant.2009.3.35

Abstract

The class of standard braided vector spaces, introduced by Andruskiewitsch and the author in 2007 to understand the proof of a theorem of Heckenberger, is slightly more general than the class of braided vector spaces of Cartan type. In the present paper, we classify standard braided vector spaces with finite-dimensional Nichols algebra. For any such braided vector space, we give a PBW basis, a closed formula of the dimension and a presentation by generators and relations of the associated Nichols algebra.

Keywords

quantized enveloping algebras, Nichols algebras, automorphisms of noncommutative algebras, pointed Hopf algebras

Mathematical Subject Classification 2000

Primary: 17B37

Secondary: 16W20, 16W30

Milestones

Received: 3 April 2008

Revised: 2 October 2008

Accepted: 11 November 2008

Published: 1 February 2009

Authors

Iván Ezequiel Angiono
Universidad Nacional of Córdoba Facultad of Matemática, Astronomía y Física Medina Allende s/n, Ciudad Universitaria 5000 Córdoba Argentina

Vol. 3, No. 1, 2009