Document Details Document Type : Article In Journal  Document Title : Left Hopf Algebras and Self Duality Left Hopf Algebras and Self Duality   Subject : Mthematics  Document Language : English  Abstract : In this paper, we introduce the concept of a left bicrossproduct Hopfalgebra associated to a factorization of a finite group X into a subgroupG and a subsemigroup M. Moreover, we show that for a left Hopf algebraH = kM  k(G) associated to a factorization X = GM of a groupX into a subgroup G and a subsemigroup M with identity and leftinverse property, there is a left Hopf algebra isomorphism H → H∗which sends basis elements to basis elements can be constructed from afactor-reversing isomorphism of X = GM and vise versa.  ISSN : 1312-7594  Journal Name : International Mathematical Forum  Volume : 4  Issue Number : 45-48  Publishing Year : 2009 AH 2009 AD  Article Type : Article  Added Date : Saturday, January 30, 2010  Researchers Researcher Name (Arabic) Researcher Name (English) Researcher Type Dr Grade Email محمد موسى الشمراني Al-Shomrani, M M Researcher Doctorate malshomrani@hotmail.com هتون شعيب Shoaib, H Researcher Master   Files File Name Type Description  24948.pdf pdf Abstract Back To Researches Page