Erhard Neher's Books

Steinberg Groups for Jordan Pairs

By: Ottmar Loos,Erhard Neher

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Steinberg Groups for Jordan Pairs

By: Ottmar Loos,Erhard Neher

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.

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Page Count

470

Publisher

Springer Nature

Published Date

ISBN 10

1071602640

ISBN 13

9781071602645

Locally Finite Root Systems

By: Ottmar Loos,Erhard Neher

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Locally Finite Root Systems

By: Ottmar Loos,Erhard Neher

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.

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Page Count

232

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821835467

ISBN 13

9780821835463

Jordan Triple Systems by the Grid Approach

By: Erhard Neher

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Jordan Triple Systems by the Grid Approach

By: Erhard Neher

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.

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Page Count

206

Publisher

Springer

Published Date

ISBN 10

354047921X

ISBN 13

9783540479215

Jordan Triple Systems by the Grid Approach

By: Erhard Neher

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Jordan Triple Systems by the Grid Approach

By: Erhard Neher

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Page Count

206

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Springer

Published Date

ISBN 10

354047921X

ISBN 13

9783540479215

Geometric Representation Theory and Extended Affine Lie Algebras

By: Erhard Neher,Alistair Savage,Weiqiang Wang

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Geometric Representation Theory and Extended Affine Lie Algebras

By: Erhard Neher,Alistair Savage,Weiqiang Wang

This text presents lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the developments in Lie algebras and representation theory in the last two decades.

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Page Count

213

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821871617

ISBN 13

9780821871614

Steinberg Groups for Jordan Pairs

By: Ottmar Loos,Erhard Neher

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Steinberg Groups for Jordan Pairs

By: Ottmar Loos,Erhard Neher

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Page Count

470

Publisher

Springer Nature

Published Date

ISBN 10

1071602640

ISBN 13

9781071602645

Geometric Representation Theory and Extended Affine Lie Algebras

By: Erhard Neher,Alistair Savage,Weiqiang Wang

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Geometric Representation Theory and Extended Affine Lie Algebras

By: Erhard Neher,Alistair Savage,Weiqiang Wang

Lie theory has connections to many other disciplines such as geometry, number theory, mathematical physics, and algebraic combinatorics. The interaction between algebra, geometry and combinatorics has proven to be extremely powerful in shedding new light on each of these areas. This book presents the lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the exciting developments in Lie algebras and representation theory in the last two decades. It includes topics such as geometric realizations of irreducible representations in three different approaches, combinatorics and geometry of canonical and crystal bases, finite $W$-algebras arising as the quantization of the transversal slice to a nilpotent orbit, structure theory of extended affine Lie algebras, and representation theory of affine Lie algebras at level zero. This book will be of interest to mathematicians working in Lie algebras and to graduate students interested in learning the basic ideas of some very active research directions. The extensive references in the book will be helpful to guide non-experts to the original sources.

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Page Count

226

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082185237X

ISBN 13

9780821852378

Locally Finite Root Systems

By: Ottmar Loos,Erhard Neher

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Locally Finite Root Systems

By: Ottmar Loos,Erhard Neher

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.

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Page Count

236

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821865331

ISBN 13

9780821865330

Book's by Erhard Neher

Steinberg Groups for Jordan Pairs

Steinberg Groups for Jordan Pairs

Locally Finite Root Systems

Locally Finite Root Systems

Jordan Triple Systems by the Grid Approach

Jordan Triple Systems by the Grid Approach

Jordan Triple Systems by the Grid Approach

Jordan Triple Systems by the Grid Approach

Geometric Representation Theory and Extended Affine Lie Algebras

Geometric Representation Theory and Extended Affine Lie Algebras

Steinberg Groups for Jordan Pairs

Steinberg Groups for Jordan Pairs

Geometric Representation Theory and Extended Affine Lie Algebras

Geometric Representation Theory and Extended Affine Lie Algebras

Locally Finite Root Systems

Locally Finite Root Systems

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