Jordan Triple Systems By The Grid Approach
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Jordan Triple Systems By The Grid Approach
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Author : Erhard Neher
language : en
Publisher: Springer
Release Date : 2006-11-15
Jordan Triple Systems By The Grid Approach written by Erhard Neher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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
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Author : Erhard Neher
language : en
Publisher:
Release Date : 1987
Jordan Triple Systemes By The Grid Approach written by Erhard Neher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Jordan Triple Systems In Complex And Functional Analysis
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Author : José M. Isidro
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-12-09
Jordan Triple Systems In Complex And Functional Analysis written by José M. Isidro and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-09 with Education categories.
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
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Author : Ottmar Loos
language : en
Publisher: Springer Nature
Release Date : 2020-01-10
Steinberg Groups For Jordan Pairs written by Ottmar Loos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-10 with Mathematics categories.
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
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Author : Wilhelm Kaup
language : en
Publisher: Walter de Gruyter
Release Date : 2011-05-02
Jordan Algebras written by Wilhelm Kaup and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-02 with Mathematics categories.
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.
A Taste Of Jordan Algebras
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Author : Kevin McCrimmon
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-29
A Taste Of Jordan Algebras written by Kevin McCrimmon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-29 with Mathematics categories.
This book describes the history of Jordan algebras and describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov. Jordan algebras crop up in many surprising settings, and find application to a variety of mathematical areas. No knowledge is required beyond standard first-year graduate algebra courses.
Encyclopaedia Of Mathematics Supplement Iii
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-23
Encyclopaedia Of Mathematics Supplement Iii written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-23 with Mathematics categories.
This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
Non Associative Algebras And Related Topics
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Author : Helena Albuquerque
language : en
Publisher: Springer Nature
Release Date : 2023-07-28
Non Associative Algebras And Related Topics written by Helena Albuquerque and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-28 with Mathematics categories.
This proceedings volume presents a selection of peer-reviewed contributions from the Second Non-Associative Algebras and Related Topics (NAART II) conference, which was held at the University of Coimbra, Portugal, from July 18–22, 2022. The conference was held in honor of mathematician Alberto Elduque, who has made significant contributions to the study of non-associative structures such as Lie, Jordan, and Leibniz algebras. The papers in this volume are organized into four parts: Lie algebras, superalgebras, and groups; Leibniz algebras; associative and Jordan algebras; and other non-associative structures. They cover a variety of topics, including classification problems, special maps (automorphisms, derivations, etc.), constructions that relate different structures, and representation theory. One of the unique features of NAART is that it is open to all topics related to non-associative algebras, including octonion algebras, composite algebras, Banach algebras, connections with geometry, applications in coding theory, combinatorial problems, and more. This diversity allows researchers from a range of fields to find the conference subjects interesting and discover connections with their own areas, even if they are not traditionally considered non-associative algebraists. Since its inception in 2011, NAART has been committed to fostering cross-disciplinary connections in the study of non-associative structures.
Locally Finite Root Systems
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Author : Ottmar Loos
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Locally Finite Root Systems written by Ottmar Loos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
We develop the basic theory of root systems $R$ in a real vector space $X$ which are defined in analogy to the usual finite root systems, except that finiteness is replaced by local finiteness: the intersection of $R$ with every finite-dimensional subspace of $X$ is finite. The main topics are Weyl groups, parabolic subsets and positive systems, weights, and gradings.
Non Associative Algebra And Its Applications
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Author : Santos González
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Associative Algebra And Its Applications written by Santos González and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume contains the proceedings of the Third International Conference on Non-Associative Algebra and Its Applications, held in Oviedo, Spain, July 12--17, 1993. The conference brought together specialists from all over the world who work in this interesting and active field, which is currently enjoying much attention. All aspects of non-associative algebra are covered. Topics range from purely mathematical subjects to a wide spectrum of applications, and from state-of-the-art articles to overview papers. This collection will point the way for further research for many years to come. The volume is of interest to researchers in mathematics as well as those whose work involves the application of non-associative algebra in such areas as physics, biology and genetics.