Hopf ideals in a universal Hopf algebra, with applications

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" Hopf ideals in a universal Hopf algebra, with applications "
H. M. Mohammad

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	1113276
Doc. No	:	TLpq304247278
Main Entry	:	H. M. Mohammad
Title & Author	:	Hopf ideals in a universal Hopf algebra, with applications\ H. M. Mohammad
College	:	Colorado State University
Date	:	1996
student score	:	1996
Degree	:	Ph.D.
Page No	:	73
Abstract	:	We use the Bullett-Macdonald formulation of the Adem relations to construct an integer lift usdU/{\cal I}usd of the mod-2 Steenrod squares, and show that usdU/{\cal I}usd is a Hopf algebra. We extend scalars to obtain an algebra usd{\cal A}\sb2(R)usd over any commutative ring R, and show for usdR = \doubqusd that usd{\cal A}\sb2(\doubq)usd is a polynomial algebra over usd\doubqusd on one generator. The first chapter gives an overview of Hopf algebras and a study of a free associative, noncommutative free algebra U generated by the symbols usdX\sb1,X\sb2,\...usd In the second chapter, we define the term "curve", and construct a power series algebra generated by composing curves with integer polynomials. Our construction of the algebra differs from that of previous authors in the sense that we may "substitute" in polynomials with nonzero constant terms. We conclude the chapter with some calculations used later in Chapter Three to prove that usd{\cal I}usd is a coalgebra ideal of U.
Subject	:	Adem relations
	:	Mathematics
	:	Pure sciences
	:	Steenrod algebra
	:	topology