Classifying complements for Hopf algebras and Lie algebras

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• 作者：A.L. Agore ; G. Militaru
• 关键词：16T05 ; 16S40
• 刊名：Journal of Algebra
• 出版年：2013
• 出版时间：1 October, 2013
• 年：2013
• 卷：391
• 期：Complete
• 页码：193-208
• 全文大小：300 K

文摘

Let be a given extension of Hopf (respectively Lie) algebras. We answer the classifying complements problem (CCP) which consists of describing and classifying all complements of A in E. If H is a given complement then all the other complements are obtained from H by a certain type of deformation. We establish a bijective correspondence between the isomorphism classes of all complements of A in E and a cohomological type object , where is the matched pair associated to H. The factorization index is introduced as a numerical measure of the (CCP). For two n-th roots of unity we construct a -dimensional Hopf algebra whose factorization index over the group algebra is arbitrary large.