arrangements of hyperplanes grundlehren der mathematischen wissenschaften

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Arrangements Of Hyperplanes

Author : Peter Orlik
ISBN : 9783662027721
Genre : Mathematics
File Size : 56. 8 MB
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An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space. Arrangements have emerged independently as important objects in various fields of mathematics such as combinatorics, braids, configuration spaces, representation theory, reflection groups, singularity theory, and in computer science and physics. This book is the first comprehensive study of the subject. It treats arrangements with methods from combinatorics, algebra, algebraic geometry, topology, and group actions. It emphasizes general techniques which illuminate the connections among the different aspects of the subject. Its main purpose is to lay the foundations of the theory. Consequently, it is essentially self-contained and proofs are provided. Nevertheless, there are several new results here. In particular, many theorems that were previously known only for central arrangements are proved here for the first time in completegenerality. The text provides the advanced graduate student entry into a vital and active area of research. The working mathematician will findthe book useful as a source of basic results of the theory, open problems, and a comprehensive bibliography of the subject.

Topics In Hyperplane Arrangements

Author : Marcelo Aguiar
ISBN : 9781470437114
Genre : Algebraic spaces
File Size : 85. 85 MB
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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 Möbius 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.

Arrangements

Author : Peter Orlik
ISBN : UOM:39015050696882
Genre : Mathematics
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The Face Semigroup Algebra Of A Hyperplane Arrangement

Author : Franco Valentino Saliola
ISBN : CORNELL:31924105489607
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Tokyo Journal Of Mathematics

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ISBN : UCSD:31822036058493
Genre : Mathematics
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Journal Of Mathematical Sciences The University Of Tokyo

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ISBN : UOM:39015053956283
Genre : Mathematics
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Bulletin Of The Belgian Mathematical Society Simon Stevin

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ISBN : UOM:39015068689705
Genre : Mathematics
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Annales Scientifiques De L Cole Normale Sup Rieure

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ISBN : UOM:39015049389904
Genre : Mathematics
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Honam Mathematical Journal

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ISBN : UOM:39015059093495
Genre : Mathematics
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Bulletin Of The Korean Mathematical Society

Author : Taehan Suhakhoe
ISBN : UCSD:31822036001410
Genre : Mathematics
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