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Twin Buildings and Applications to S-Arithmetic Groups

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 703/5 ( reviews)

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Book Synopsis Twin Buildings and Applications to S-Arithmetic Groups by : Peter Abramenko

Download or read book Twin Buildings and Applications to S-Arithmetic Groups written by Peter Abramenko. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: This book is addressed to mathematicians and advanced students interested in buildings, groups and their interplay. Its first part introduces - presupposing good knowledge of ordinary buildings - the theory of twin buildings, discusses its group-theoretic background (twin BN-pairs), investigates geometric aspects of twin buildings and applies them to determine finiteness properties of certain S-arithmetic groups. This application depends on topological properties of some subcomplexes of spherical buildings. The background of this problem, some examples and the complete solution for all "sufficiently large" classical buildings are covered in detail in the second part of the book.

Finiteness Properties of Arithmetic Groups Acting on Twin Buildings

2014-07-16 Mathematics
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Release : 2014-07-16
Genre : Mathematics
Kind : eBook
Book Rating : 770/5 ( reviews)

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Book Synopsis Finiteness Properties of Arithmetic Groups Acting on Twin Buildings by : Stefan Witzel

Download or read book Finiteness Properties of Arithmetic Groups Acting on Twin Buildings written by Stefan Witzel. This book was released on 2014-07-16. Available in PDF, EPUB and Kindle. Book excerpt: Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places. While the proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory of twin buildings.

Finiteness Properties of Arithmetic Groups Acting on Twin Buildings

2014-07-20 Mathematics
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Release : 2014-07-20
Genre : Mathematics
Kind : eBook
Book Rating : 789/5 ( reviews)

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Book Synopsis Finiteness Properties of Arithmetic Groups Acting on Twin Buildings by : Stefan Witzel

Download or read book Finiteness Properties of Arithmetic Groups Acting on Twin Buildings written by Stefan Witzel. This book was released on 2014-07-20. Available in PDF, EPUB and Kindle. Book excerpt: Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places. While the proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory of twin buildings.

Tits Buildings and the Model Theory of Groups

2002-01-03 Mathematics
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Release : 2002-01-03
Genre : Mathematics
Kind : eBook
Book Rating : 634/5 ( reviews)

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Book Synopsis Tits Buildings and the Model Theory of Groups by : Katrin Tent

Download or read book Tits Buildings and the Model Theory of Groups written by Katrin Tent. This book was released on 2002-01-03. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to buildings and their geometries with emphasis on model theoretic constructions, covering recent developments.

Buildings, Finite Geometries and Groups

2011-11-13 Mathematics
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Release : 2011-11-13
Genre : Mathematics
Kind : eBook
Book Rating : 095/5 ( reviews)

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Book Synopsis Buildings, Finite Geometries and Groups by : N.S. Narasimha Sastry

Download or read book Buildings, Finite Geometries and Groups written by N.S. Narasimha Sastry. This book was released on 2011-11-13. Available in PDF, EPUB and Kindle. Book excerpt: This is the Proceedings of the ICM 2010 Satellite Conference on “Buildings, Finite Geometries and Groups” organized at the Indian Statistical Institute, Bangalore, during August 29 – 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, etc. These articles reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective the authors bring in their articles on the current developments and the major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these areas.

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