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001 978-3-540-38864-7
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008 121227s1988 gw | s |||| 0|eng d
020 _a9783540388647
_9978-3-540-38864-7
024 7 _a10.1007/BFb0079295
_2doi
050 4 _aQA252.3
050 4 _aQA387
072 7 _aPBG
_2bicssc
072 7 _aMAT014000
_2bisacsh
072 7 _aPBG
_2thema
082 0 4 _a512.55
_223
082 0 4 _a512.482
_223
100 1 _aSeligman, George B.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aConstructions of Lie Algebras and their Modules
_h[electronic resource] /
_cby George B. Seligman.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1988.
300 _aVIII, 196 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1300
505 0 _aAn introductory example: sl(n,D) -- General considerations -- Involutorial algebras and modules for their skew elements -- Construction of modules with prescribed relative highest weights, for the isotropic algebras of chapter 3 -- Construction of exceptional algebras from quadratic forms -- Representations of exceptional algebras constructed from quadratic forms -- Non-reduced excepticnal algebras with a one-dimensional root space -- Construction of modules for the super-exceptional algebras of rank one -- Complements.
520 _aThis book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. The book is intended for researchers and students of algebraic Lie theory, as well as for other researchers who are seeking explicit realizations of algebras or modules. It will probably be more useful as a resource to be dipped into, than as a text to be worked straight through.
650 0 _aTopological Groups.
650 1 4 _aTopological Groups, Lie Groups.
_0http://scigraph.springernature.com/things/product-market-codes/M11132
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540189732
776 0 8 _iPrinted edition:
_z9783662195697
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1300
856 4 0 _uhttps://doi.org/10.1007/BFb0079295
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10544
_d10544