Connected Hopf algebras of finite Gelfand-Kirillov dimension

Following the seminal work of Zhuang, connected Hopf algebras of finite GK-dimension over algebraically closed fields of characteristic zero have been the subject of several recent papers. This thesis is concerned with continuing this line of research and promoting connected Hopf algebras as a natural, intricate and interesting class of algebras. We begin by discussing the theory of connected Hopf algebras which are either commutative or cocommutative, and then proceed to review the modern theory of arbitrary connected Hopf algebras of finite GK-dimension initiated by Zhuang. We next focus on the (left) coideal subalgebras of connected Hopf algebras of finite GK-dimension. They are shown to be deformations of commutative polynomial algebras. A number of homological properties follow immediately from this fact. Further properties are described, examples are considered and invariants are constructed. A connected Hopf algebra is said to be "primitively thick" if the difference between its GK-dimension and the vector-space dimension of its primitive space is precisely one . Building on the results of Wang, Zhang and Zhuang,, we describe a method of constructing such a Hopf algebra, and as a result obtain a host of new examples of such objects. Moreover, we prove that such a Hopf algebra can never be isomorphic to the enveloping algebra of a semisimple Lie algebra, nor can a semisimple Lie algebra appear as its primitive space. It has been asked in the literature whether connected Hopf algebras of finite GK-dimension are always isomorphic as algebras to enveloping algebras of Lie algebras. We provide a negative answer to this question by constructing a counterexample of GK-dimension 5. Substantial progress was made in determining the order of the antipode of a finite dimensional pointed Hopf algebra by Taft and Wilson in the 1970s. Our final main result is to show that the proof of their result can be generalised to give an analogous result for arbitrary pointed Hopf algebras.

Richard Yates: re-writing postwar American culture

This thesis explores the fiction of American author Richard Yates to propose that his work provides an insistent questioning and alternative vision of postwar American culture. Such an approach is informed by a revisionist account of four distinct yet interconnected areas of postwar culture: the role of the non-heroic soldier stepping in and out of World War II; suburbanisation and fashioning of anti-suburban performance; demarcation of gender roles and unraveling of sexual conservatism in the 1950s; consideration of what constituted the normative within postwar discourse and representations of mental illness in Yates’ work. These four spheres of interest form the backbone to this study in its combined aim of reclaiming Yates’ fiction in line with a more progressive historical framework while shaping a new critical appreciation of his fiction. Such analysis will be primed by an opening discussion that illustrates how Yates’ fiction has frequently been ensconced in a limited interpretative lens: an approach, that I argue, has kept Yates on the periphery of the canon and ultimately resulted in the neglect of an author who provided a rich, progressive and historically significant dialogue of postwar American life. This PhD arrives at a point when Yatesian scholarship is finally gaining momentum after the cumulative impact of a comprehensive biography, a faithful film adaptation of his seminal text Revolutionary Road (1961), plus the recent re-issue of his catalogue of work. An assessment as to why he remained on the margins of success for the duration of his career is therefore of pressing interest in light of this recent critical and commercial recognition.