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Topics in hyperplane arrangements / (Record no. 424602)

MARC details
000 -LEADER
fixed length control field 03475cam a2200289 i 4500
001 - CONTROL NUMBER
control field 138312
003 - CONTROL NUMBER IDENTIFIER
control field ISI Library, Kolkata
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20180511121617.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 170420s2017 riua b 001 0 eng
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781470437114 (alk. paper)
040 ## - CATALOGING SOURCE
Original cataloging agency ISI Library
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 510MS
Edition number 23
Item number Am512
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Aguiar, Marcelo,
Relator term author
245 10 - TITLE STATEMENT
Title Topics in hyperplane arrangements /
Statement of responsibility, etc Marcelo Aguiar and Swapneel Mahajan.
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc Providence :
Name of publisher, distributor, etc American Mathematical Society,
Date of publication, distribution, etc ©2017.
300 ## - PHYSICAL DESCRIPTION
Extent xxiv, 611 pages :
Other physical details illustrations ;
Dimensions 27 cm.
490 0# - SERIES STATEMENT
Series statement Mathematical surveys and monographs ;
Volume number/sequential designation v 226.
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Includes bibliographical references and index.
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note 1. Hyperplane arrangements --<br/>2. Cones --<br/>3. Lunes --<br/>4. Category of lunes --<br/>5. Reflection arrangements --<br/>6. Braid arrangement and related examples --<br/>7. Descent and lune equations --<br/>8. Distance functions and Varchenko matrix --<br/>9. Birkhoff algebra and Tits algebra --<br/>10. Lie and Zie elements --<br/>11. Eulerian idempotents --<br/>12. Diagonalizability and characteristic elements --<br/>13. Loewy series and Peirce decompositions --<br/>14. Dynkin idempotents --<br/>15. Incidence algebras --<br/>16. Invariant Birkhoff algebra and invariant Tits algebra --<br/> Appendix A. Regular cell complexes --<br/> Appendix B. Posets --<br/> Appendix C. Incidence algebras of posets --<br/> Appendix D. Algebras and molecules --<br/> Appendix E. Bands.
520 ## - SUMMARY, ETC.
Summary, etc 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.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Incidence algebras.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Algebraic spaces.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Hyperspace.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Plane geometry.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Mahajan, Swapneel,
Relator term author
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme Dewey Decimal Classification
Koha item type Books
Holdings
Lost status Not for loan Home library Current library Date acquired Source of acquisition Cost, normal purchase price Full call number Accession Number Koha item type
    ISI Library, Kolkata ISI Library, Kolkata 23/03/2018 279 9328.68 510MS Am512 138312 Books
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