04457nam 22006615 450 991037025150332120230105193623.01-0716-0264-010.1007/978-1-0716-0264-5(CKB)4900000000505239(DE-He213)978-1-0716-0264-5(MiAaPQ)EBC6012481(PPN)242844723(EXLCZ)99490000000050523920200110d2019 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierSteinberg Groups for Jordan Pairs /by Ottmar Loos, Erhard Neher1st ed. 2019.New York, NY :Springer New York :Imprint: Birkhäuser,2019.1 online resource (XII, 458 p. 2 illus. in color.)Progress in Mathematics,0743-1643 ;3321-0716-0262-4 Includes bibliographical references and index.Preface -- Notation and Conventions -- Groups with Commutator Relations -- Groups Associated with Jordan Pairs -- Steinberg Groups for Peirce Graded Jordan Pairs -- Jordan Graphs -- Steinberg Groups for Root Graded Jordan Pairs -- Central Closedness -- Bibliography -- Subject Index -- Notation Index.Steinberg groups, originating in the work of R. Steinberg on Chevalley groups in the nineteen sixties, are groups defined by generators and relations. The main examples are groups modelled on elementary matrices in the general linear, orthogonal and symplectic group. Jordan theory started with a famous article in 1934 by physicists P. Jordan and E. Wigner, and mathematician J. v. Neumann with the aim of developing new foundations for quantum mechanics. Algebraists soon became interested in the new Jordan algebras and their generalizations: Jordan pairs and triple systems, with notable contributions by A. A. Albert, N. Jacobson and E. Zel'manov. 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.Progress in Mathematics,0743-1643 ;332Nonassociative ringsRings (Algebra)K-theoryNumber theoryGroup theoryNon-associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11116K-Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11086Number Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Group Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Nonassociative rings.Rings (Algebra).K-theory.Number theory.Group theory.Non-associative Rings and Algebras.K-Theory.Number Theory.Group Theory and Generalizations.512.24Loos Ottmarauthttp://id.loc.gov/vocabulary/relators/aut59242Neher Erhard1949-authttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910370251503321Steinberg Groups for Jordan Pairs2509299UNINA