03497nam 2200637 450 991078885920332120170822144446.01-4704-0587-3(CKB)3360000000465157(EBL)3114188(SSID)ssj0000888951(PQKBManifestationID)11479151(PQKBTitleCode)TC0000888951(PQKBWorkID)10866175(PQKB)10554145(MiAaPQ)EBC3114188(RPAM)16288842(PPN)195418638(EXLCZ)99336000000046515720150417h20102010 uy 0engur|n|---|||||txtccrThe generalised Jacobson-Morosov theorem /Peter O'SullivanProvidence, Rhode Island :American Mathematical Society,2010.©20101 online resource (120 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 207, Number 973"Volume 207, Number 973 (third of 5 numbers)."0-8218-4895-X Includes bibliographical references and index.""Contents""; ""Introduction""; ""Notation and Terminology""; ""Chapter 1. Affine Group Schemes over a Field of Characteristic Zero""; ""1.1. Groups""; ""1.2. Representations""; ""1.3. Spaces of homomorphisms""; ""Chapter 2. Universal and Minimal Reductive Homomorphisms""; ""2.1. Reductive homomorphisms""; ""2.2. Universal reductive homomorphisms""; ""2.3. Minimal reductive homomorphisms""; ""Chapter 3. Groups with Action of a Proreductive Group""; ""3.1. Simply connected groups""; ""3.2. Groups with action of a group""; ""3.3. Equivariant homomorphisms""""Chapter 4. Families of Minimal Reductive Homomorphisms""""4.1. Stratifications and constructible subsets""; ""4.2. Reductive group schemes""; ""4.3. Universal families""; ""Bibliography""; ""Index"""The author considers homomorphisms H to K from an affine group scheme H over a field k of characteristic zero to a proreductive group K. Using a general categorical splitting theorem, Andrâe and Kahn proved that for every H there exists such a homomorphism which is universal up to conjugacy. The author gives a purely group-theoretic proof of this result. The classical Jacobson-Morosov theorem is the particular case where H is the additive group over k. As well as universal homomorphisms, the author considers more generally homomorphisms H to K which are minimal, in the sense that H to K factors through no proper proreductive subgroup of K. For fixed H, it is shown that the minimal H to K with K reductive are parametrised by a scheme locally of finite type over k."--Publisher's description.Memoirs of the American Mathematical Society ;Volume 207, Number 973.Linear algebraic groupsGroup theoryCommutative ringsAlgebraic varietiesGeometry, AlgebraicLinear algebraic groups.Group theory.Commutative rings.Algebraic varieties.Geometry, Algebraic.512/.5O'Sullivan Peter1951-1582092MiAaPQMiAaPQMiAaPQBOOK9910788859203321The generalised Jacobson-Morosov theorem3864139UNINA