عنوان

Hopf ideals in a universal Hopf algebra, with applications

Number

TLpq304247278

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Hopf ideals in a universal Hopf algebra, with applications

General Material Designation

[Thesis]

First Statement of Responsibility

H. M. Mohammad

Name of Publisher, Distributor, etc.

Colorado State University

Date of Publication, Distribution, etc.

1996

Specific Material Designation and Extent of Item

73

Dissertation or thesis details and type of degree

Ph.D.

Body granting the degree

Colorado State University

Text preceding or following the note

1996

Text of Note

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.

Adem relations

Mathematics

Pure sciences

Steenrod algebra

topology

H. M. Mohammad

Electronic name

p

[Thesis]

276903

a

Y