Topics in hyperplane arrangements

Description

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 ca.  Read more... Abstract: Studies the interplay between various algebraic, geometric and combinatorial aspects of real hyperplane arrangements. This volume provides a careful, organised 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.  Read more... Content: Hyperplane arrangements Cones Lunes Category of lunes Reflection arrangements Braid arrangement and related examples Descent and lune equations Distance functions and Varchenko matrix Birkhoff algebra and Tits algebra Lie and Zie elements Eulerian idempotents Diagonalizability and characteristic elements Loewy series and Peirce decompositions Dynkin idempotents Incidence algebras Invariant Birkhoff algebra and invariant Tits algebra Regular cell complexes Posets Incidence algebras of posets Algebras and modules Bands.