Lifting of Quantum Linear Spaces and Pointed Hopf Algebras of order p^3

Simple item page
dc.creatorAndruskiewitsch, N.
dc.creatorSchneider, H. -J.
dc.date1998-03-13
dc.date.accessioned2026-07-07T05:24:05Z
dc.date.available2026-07-07T05:24:05Z
dc.descriptionWe propose the following principle to study pointed Hopf algebras, or more generally, Hopf algebras whose coradical is a Hopf subalgebra. Given such a Hopf algebra A, consider its coradical filtration and the associated graded coalgebra grad(A). Then grad(A) is a graded Hopf algebra, since the coradical A_0 of A is a Hopf subalgebra. In addition, there is a projection π: grad(A) \to A_0; let R be the algebra of coinvariants of π. Then, by a result of Radford and Majid, R is a braided Hopf algebra and grad(A) is the bosonization (or biproduct) of R and A_0: grad(A) is isomorphic to (R # A_0). The principle we propose to study A is first to study R, then to transfer the information to grad(A) via bosonization, and finally to lift to A. In this article, we apply this principle to the situation when R is the simplest braided Hopf algebra: a quantum linear space. As consequences of our technique, we obtain the classification of pointed Hopf algebras of order p^3 (p an odd prime) over an algebraically closed field of characteristic zero; with the same hypothesis, the characterization of the pointed Hopf algebras whose coradical is abelian and has index p or p^2; and an infinite family of pointed, non-isomorphic, Hopf algebras of the same dimension. This last result gives a negative answer to a conjecture of I. Kaplansky.
dc.descriptionAmsTeX, 28 pages. To be published in J. of Algebra
dc.identifierhttps://arxiv.org/abs/math/9803058
dc.identifierhttp://arxiv.org/abs/math/9803058
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76696
dc.subjectQuantum Algebra
dc.titleLifting of Quantum Linear Spaces and Pointed Hopf Algebras of order p^3
dc.typetext

Files

Collections

arXiv