Elementary groups and stability for Jordan pairs

DOI10.1007/BF00965460zbMath0835.17021MaRDI QIDQ1895845

Ottmar Loos

Publication date: 16 April 1996

Published in: \(K\)-Theory (Search for Journal in Brave)

zbMATH Keywords

stabilityJordan algebrasJordan pairsPeirce decompositionsprojective elementary groupquasiinvertibility for quadruples of elementsstable rank condition

Mathematics Subject Classification ID

Associated groups, automorphisms of Jordan algebras (17C30) Associated geometries of Jordan algebras (17C37)

Related Items

Generalized projective geometries: general theory and equivalence with Jordan structures ⋮ Left Quotient Associative Pairs and Morita Invariant Properties ⋮ Special Moufang sets coming from quadratic Jordan division algebras ⋮ Projective completions of Jordan pairs. I: The generalized projective geometry of a Lie algebra ⋮ The Capelli Operator and the Centroid of Rectangular Matrices ⋮ Cubic Action of a Rank one Group ⋮ Finite \(\mathbb{Z}\)-gradings of simple associative algebras. ⋮ The ideal of Lesieur-Croisot elements of Jordan pairs ⋮ Inner ideals and intrinsic subspaces of linear pair geometries ⋮ Jordan Structures and Non-Associative Geometry ⋮ EXCHANGE MORITA RINGS ⋮ Nonassociative algebras and groups with property (T) ⋮ Cyclic orders defined by ordered jordan algebras ⋮ SIMPLE, PRIMITIVE, AND STRONGLY PRIME JORDAN 3-GRADED LIE ALGEBRAS ⋮ Moufang sets from groups of mixed type ⋮ Tits-Kantor-Koecher Superalgebras of Jordan Superpairs Covered by Grids ⋮ Steinberg groups for Jordan pairs ⋮ Fountain-Gould left orders for associative pairs. ⋮ Chevalley groups of type E7 in the 56-dimensional representation ⋮ Generalized flag geometries and manifolds associated to short \(\mathbb Z\)-graded Lie algebras in arbitrary dimension ⋮ Elementary subgroups of isotropic reductive groups ⋮ Jordan cubes and associative powers. ⋮ Associative systems generated by symmetric elements of a system with involution ⋮ Goldie theorems for associative pairs ⋮ Steinberg groups for Jordan pairs: an introduction with open problems ⋮ Jordan pairs and Hopf algebras ⋮ Associative systems of left quotients. ⋮ Elementary groups and invertibility for kantor pairs ⋮ The geometry of null systems, Jordan algebras and von Staudt's theorem.

Cites Work

• Bass's first stable range condition
• On the socle of a Jordan pair
• Stable range and linear groups for alternative rings
• Complementation of inner ideals in Jordan pairs
• General symbols and presentations of elementary linear groups.
• On algebraic groups defined by Jordan pairs
• Decomposition of projective spaces defined by unit-regular jordan pairs
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