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Fusion systems in algebra and topology par Aschbacher, Michael Publication : Cambridge | New York Cambridge University Press 2011 . vi, 320 pages , "A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. The book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians"-- 23 cm. Date : 2011 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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How groups grow par Mann, Avinoam Publication : Cambridge, UK | New York Cambridge University Press 2012 . ix, 199 pages 23 cm. Date : 2012 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Moonshine : the first quarter century and beyond : proceedings of a workshop on the moonshine conjectures and vertex algebras   Publication : Cambridge | New York Cambridge University Press 2010 . xii, 403 pages , "In 1979, John Conway and Simon Norton's famous paper, 'Monstrous Moonshine', outlined the remarkable connection between the monster group M and the theory of modular functions. The search for an explanation of this phenomenon involved the development and application of diverse areas of mathematics, including (generalized) Kac-Moody algebras, vertex (operator) algebras, automorphic forms and elliptic cohomology, together with string and conformal field theory from theoretical physics. This volume consists of seventeen papers based on talks presented at a workshop held to mark the anniversary of 'Monstrous Moonshine'. Containing a mixture of expository and current research material, they illustrate its extensive impact and reflect the broad range of research activity that has stemmed from the Moonshine conjectures. Potential directions for future development are also discussed"--Provided by publisher. | "Modular Tensor Categories (MTCs for short)[1, 16] have attracted much attentionin recent years, which is due to the recognition of their importance in bothpure mathematics - 3-dimensional topology, representations of Vertex OperatorAlgebras (VOAs for short) - and theoretical physics"--Provided by publisher. 23 cm. Date : 2010 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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