Steinberg Groups For Jordan Pairs

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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.

Interactions Of Quantum Affine Algebras With Cluster Algebras Current Algebras And Categorification

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Author : Jacob Greenstein
language : en
Publisher: Springer Nature
Release Date : 2022-03-11

Interactions Of Quantum Affine Algebras With Cluster Algebras Current Algebras And Categorification written by Jacob Greenstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-11 with Mathematics categories.

This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.

Property T For Groups Graded By Root Systems

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Author : Mikhail Ershov
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-09-25

Property T For Groups Graded By Root Systems written by Mikhail Ershov 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 2017-09-25 with Mathematics categories.

The authors introduce and study the class of groups graded by root systems. They prove that if is an irreducible classical root system of rank and is a group graded by , then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of . As the main application of this theorem the authors prove that for any reduced irreducible classical root system of rank and a finitely generated commutative ring with , the Steinberg group and the elementary Chevalley group have property . They also show that there exists a group with property which maps onto all finite simple groups of Lie type and rank , thereby providing a “unified” proof of expansion in these groups.

Cubic Action Of A Rank One Group

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Author : Matthias Grüninger
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-08

Cubic Action Of A Rank One Group written by Matthias Grüninger and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-08 with Mathematics categories.

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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.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2008

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

Abstracts Of Papers Presented To The American Mathematical Society

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Author : American Mathematical Society
language : en
Publisher:
Release Date : 1995

Abstracts Of Papers Presented To The American Mathematical Society written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

Groups Rings Lie And Hopf Algebras

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Author : Y. Bahturin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Groups Rings Lie And Hopf Algebras written by Y. Bahturin 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 2013-12-01 with Mathematics categories.

The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

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.

Moufang Sets And Structurable Division Algebras

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Author : Lien Boelaert
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-06-10

Moufang Sets And Structurable Division Algebras written by Lien Boelaert 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 2019-06-10 with Mathematics categories.

A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they are assumed to be conjugate and to generate the whole group. It has been known for some time that every Jordan division algebra gives rise to a Moufang set with abelian root groups. The authors extend this result by showing that every structurable division algebra gives rise to a Moufang set, and conversely, they show that every Moufang set arising from a simple linear algebraic group of relative rank one over an arbitrary field k of characteristic different from 2 and 3 arises from a structurable division algebra. The authors also obtain explicit formulas for the root groups, the τ-map and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups.