Methodes en syntaxe M. Gross, Hermann, 1975, 414 pp.

Narcissism, the body and modernity The notion of narcissism is often used and misused within contemporary social theory. Whereas the concept is frequently used in discussions of moral decline and of the negative impact of consumer culture on social character, the aim of this article is instead to put forward a social psychological analysis of narcissism. Goffman’s discussion of the presentation of self in everyday life and Giddens’ theory of self-identity and modernity, are used as points of departure in an analysis of the social psychological aspects of narcissism. The main argument in the article is that it is necessary to study the contextual aspects of the construction of what is often called ”narcissistic disorders”. This implies a change of emphasis from narcissism as a general social and cultural disorder, to more specific analysis of critical situations and critical milieux. The article also contains a discussion of the relation between the ambivalent character of modernity, the cult of the body and narcissism. Examples from the gym culture are used in order to highlight some of the arguments in the article.Sociologisk Forsknings digitala arkiv</p

Spitzer's Identity and the Algebraic Birkhoff Decomposition in pQFT

In this article we continue to explore the notion of Rota-Baxter algebras in the context of the Hopf algebraic approach to renormalization theory in perturbative quantum field theory. We show in very simple algebraic terms that the solutions of the recursively defined formulae for the Birkhoff factorization of regularized Hopf algebra characters, i.e. Feynman rules, naturally give a non-commutative generalization of the well-known Spitzer's identity. The underlying abstract algebraic structure is analyzed in terms of complete filtered Rota-Baxter algebras.Comment: 19 pages, 2 figure

Generalized shuffles related to Nijenhuis and TD-algebras

Shuffle and quasi-shuffle products are well-known in the mathematics literature. They are intimately related to Loday's dendriform algebras, and were extensively used to give explicit constructions of free commutative Rota-Baxter algebras. In the literature there exist at least two other Rota-Baxter type algebras, namely, the Nijenhuis algebra and the so-called TD-algebra. The explicit construction of the free unital commutative Nijenhuis algebra uses a modified quasi-shuffle product, called the right-shift shuffle. We show that another modification of the quasi-shuffle product, the so-called left-shift shuffle, can be used to give an explicit construction of the free unital commutative TD-algebra. We explore some basic properties of TD-operators and show that the free unital commutative Nijenhuis algebra is a TD-algebra. We relate our construction to Loday's unital commutative dendriform trialgebras, including the involutive case. The concept of Rota-Baxter, Nijenhuis and TD-bialgebras is introduced at the end and we show that any commutative bialgebra provides such objects.Comment: 20 pages, typos corrected, accepted for publication in Communications in Algebr