Bimonoids for Hyperplane Arrangements, Marcelo Aguiar, Swapneel Mahajan

Автор: Marcelo Aguiar, Swapneel Mahajan
Название: Topics in Hyperplane Arrangements
ISBN: 1470437112 ISBN-13(EAN): 9781470437114
Издательство: Mare Nostrum (Eurospan)
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Цена: 141290.00 T
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Описание: This monograph studies the interplay between various algebraic, geometric and combinatorial aspects of real hyperplane arrangements. It provides a careful, organized and unified treatment of several recent developments in the field, and brings forth many new ideas and results. It has two parts, each divided into eight chapters, and five appendices with background material. Part I gives a detailed discussion on faces, flats, chambers, cones, gallery intervals, lunes and other geometric notions associated with arrangements. The Tits monoid plays a central role. Another important object is the category of lunes which generalizes the classical associative operad. Also discussed are the descent and lune identities, distance functions on chambers, and the combinatorics of the braid arrangement and related examples. Part II studies the structure and representation theory of the Tits algebra of an arrangement. It gives a detailed analysis of idempotents and Peirce decompositions, and connects them to the classical theory of Eulerian idempotents. It introduces the space of Lie elements of an arrangement which generalizes the classical Lie operad. This space is the last nonzero power of the radical of the Tits algebra. It is also the socle of the left ideal of chambers and of the right ideal of Zie elements. Zie elements generalize the classical Lie idempotents. They include Dynkin elements associated to generic half-spaces which generalize the classical Dynkin idempotent. Another important object is the lune-incidence algebra which marks the beginning of noncommutative Mobius theory. These ideas are also brought upon the study of the Solomon descent algebra. The monograph is written with clarity and in sufficient detail to make it accessible to graduate students. It can also serve as a useful reference to experts.

Автор: Alexandru Dimca
Название: Hyperplane Arrangements
ISBN: 3319562207 ISBN-13(EAN): 9783319562209
Издательство: Springer
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Цена: 60550.00 T
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Описание: Invitation to the Trip.- Hyperplane Arrangements and their Combinatorics.- Orlik-Solomon Algebras and de Rham Cohomology.- On the Topology of the Complement M(A).- Milnor Fibers and Local Systems.- Characteristic Varieties and Resonance Varieties.- Logarithmic Connections and Mixed Hodge Structures.- Free Arrangements and de Rham Cohomology of Milnor Fibers.

Автор: Anita Sch?bel
Название: Locating Lines and Hyperplanes
ISBN: 1461374286 ISBN-13(EAN): 9781461374282
Издательство: Springer
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Цена: 93160.00 T
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Описание: Line and hyperplane location problems play an important role not only in operations research and location theory, but also in computational geometry and robust statistics. Audience: The book is suitable for researchers, lecturers, and graduate students working in the fields of location theory or computational geometry.