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This reprint of a 1983 Yale graduate course makes results in modular representation theory accessible to an audience ranging from second-year graduate students to established mathematicians. Following a review of background material, the lectures examine three closely connected topics in modular representation theory of finite groups: representations rings; almost split sequences and the Auslander-Reiten quiver; and complexity and cohomology varieties, which has become a major theme in representation theory.
Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving...
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The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Kählerian geometry, and connected with many important pure mathematical branches such as affine differential geometry, homogeneous spaces and cohomology. The theory also finds deep relation to information geometry in applied mathematics. This systematic introduction to the subject first develops the fundamentals of Hessian structures on the basis of a certain pair of a flat connection and a Riemannian metric, and then describes these related fields as applications of the theory.
A comprehensive and groundbreaking collection of ideas for plant improvement Most of the world's supply of legumes is cultivated under adverse conditions that make this commercially important crop susceptible to the vagaries of nature and damaging stresses. Genetic manipulation has become a proven way for cultivators to battle these pro
This book presents the proceedings of the 13th International Congress on Nitrogen Fixation, held in Hamilton, Ontario, Canada, in July 2001. It covers molecular and biochemical aspects, plant genomics, stresses and factors limiting nitrogen fixation, and applied aspects.
Bacterial surface or secreted polysaccharides are molecules that can function as barriers to protect bacterial cells against environmental stresses, as well as act as adhesins or recognition molecules. In some cases, these molecules are immunodominant antigens eliciting a vigorous immune response, while in other cases the expression of polysacchari
This volume of Applied Mycology and Biotechnology completes the set of two volumes dedicated to the coverage of recent developments on the theme "Agriculture and Food Production". The first volume provided overview on fungal physiology, metabolism, genetics and biotechnology and highlighted their connection with particular applications to food production. The second volume examines various specific applications of mycology and fungal biotechnology to food production and processing. In the second volume coverage on two remaining areas of the theme, food crop production and applications in the foods and beverages sector, is presented.The interdisciplinary and complex nature of the subject area...
Nitrogen availability is one of the most critical factors that limits plant productivity. The largest reservoir of nitrogen is the atmosphere, but this gaseous molecular nitrogen only becomes available to plants through the biological nitrogen fixation process, which only prokaryotic cells have developed. The discovery that microbes were providing fixed nitrogen to legumes and the isolation of the first nitrogen-fixing bacteria occured at the end the 19th Century, in Louis Pasteur's time. We are now building on more than 100 years of research in this field and looking towards the 21st Century. The International Nitrogen Fixation Congress series Started more than 20 years ago. The format of this Congress is designed to gather scientists from very diverse origins, backgrounds, interests and scientific approaches and is a forum where fundamental knowledge is discussed alongside applied research. This confluence of perspectives is, we believe, extremely beneficial in raising new ideas, questions and concepts.
The Rhizobiaceae, Molecular Biology of Model Plant-Associated Bacteria. This book gives a comprehensive overview on our present molecular biological knowledge about the Rhizobiaceae, which currently can be called the best-studied family of soil bacteria. For many centuries they have attracted the attention of scientists because of their capacity to associate with plants and as a consequence also to specifically modify plant development. Some of these associations are beneficial for the plant, as is the case for the Rhizobiaceae subgroups collectively called rhizobia, which are able to fix nitrogen in a symbiosis with the plant hosts. This symbiosis results in the fonnation of root or stem no...