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Jordan Triple Systems by the Grid Approach

2006-11-15 Mathematics
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Release : 2006-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 21X/5 ( reviews)

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Book Synopsis Jordan Triple Systems by the Grid Approach by : Erhard Neher

Download or read book Jordan Triple Systems by the Grid Approach written by Erhard Neher. This book was released on 2006-11-15. Available in PDF, EPUB and Kindle. Book excerpt: Grids are special families of tripotents in Jordan triple systems. This research monograph presents a theory of grids including their classification and coordinization of their cover. Among the applications given are - classification of simple Jordan triple systems covered by a grid, reproving and extending most of the known classification theorems for Jordan algebras and Jordan pairs - a Jordan-theoretic interpretation of the geometry of the 27 lines on a cubic surface - structure theories for Hilbert-triples and JBW*-triples, the Jordan analogues of Hilbert-triples and W*-algebras which describe certain symmetric Banach manifolds. The notes are essentially self-contained and independent of the structure theory of Jordan algebras and Jordan pairs. They can be read by anyone with a basic knowledge in algebraic geometry or functional analysis. The book is intended to serve both as a reference for researchers in Jordan theory and as an introductory textbook for newcomers to the subject.

Jordan Triple Systemes by the Grid Approach

1987
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Release : 1987
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Book Synopsis Jordan Triple Systemes by the Grid Approach by : Erhard Neher

Download or read book Jordan Triple Systemes by the Grid Approach written by Erhard Neher. This book was released on 1987. Available in PDF, EPUB and Kindle. Book excerpt:

Jordan Triple Systems in Complex and Functional Analysis

2019-12-09 Education
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Release : 2019-12-09
Genre : Education
Kind : eBook
Book Rating : 836/5 ( reviews)

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Book Synopsis Jordan Triple Systems in Complex and Functional Analysis by : José M. Isidro

Download or read book Jordan Triple Systems in Complex and Functional Analysis written by José M. Isidro. This book was released on 2019-12-09. Available in PDF, EPUB and Kindle. Book excerpt: This book is a systematic account of the impressive developments in the theory of symmetric manifolds achieved over the past 50 years. It contains detailed and friendly, but rigorous, proofs of the key results in the theory. Milestones are the study of the group of holomomorphic automorphisms of bounded domains in a complex Banach space (Vigué and Upmeier in the late 1970s), Kaup's theorem on the equivalence of the categories of symmetric Banach manifolds and that of hermitian Jordan triple systems, and the culminating point in the process: the Riemann mapping theorem for complex Banach spaces (Kaup, 1982). This led to the introduction of wide classes of Banach spaces known as JB∗-triples and JBW∗-triples whose geometry has been thoroughly studied by several outstanding mathematicians in the late 1980s. The book presents a good example of fruitful interaction between different branches of mathematics, making it attractive for mathematicians interested in various fields such as algebra, differential geometry and, of course, complex and functional analysis.

Steinberg Groups for Jordan Pairs

2020-01-10 Mathematics
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Release : 2020-01-10
Genre : Mathematics
Kind : eBook
Book Rating : 640/5 ( reviews)

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Book Synopsis Steinberg Groups for Jordan Pairs by : Ottmar Loos

Download or read book Steinberg Groups for Jordan Pairs written by Ottmar Loos. This book was released on 2020-01-10. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph develops a unified theory of Steinberg groups, independent of matrix representations, based on the theory of Jordan pairs and the theory of 3-graded locally finite root systems. The development of this approach occurs over six chapters, progressing from groups with commutator relations and their Steinberg groups, then on to Jordan pairs, 3-graded locally finite root systems, and groups associated with Jordan pairs graded by root systems, before exploring the volume's main focus: the definition of the Steinberg group of a root graded Jordan pair by a small set of relations, and its central closedness. Several original concepts, such as the notions of Jordan graphs and Weyl elements, provide readers with the necessary tools from combinatorics and group theory. Steinberg Groups for Jordan Pairs is ideal for PhD students and researchers in the fields of elementary groups, Steinberg groups, Jordan algebras, and Jordan pairs. By adopting a unified approach, anybody interested in this area who seeks an alternative to case-by-case arguments and explicit matrix calculations will find this book essential.

Jordan Algebras

2011-05-02 Mathematics
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Release : 2011-05-02
Genre : Mathematics
Kind : eBook
Book Rating : 119/5 ( reviews)

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Book Synopsis Jordan Algebras by : Wilhelm Kaup

Download or read book Jordan Algebras written by Wilhelm Kaup. This book was released on 2011-05-02. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

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