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Structure and Presentations of Lie‐Type Groups
Author(s) -
Timmesfeld F. G.
Publication year - 2000
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611500012442
Subject(s) - mathematics , simple lie group , rank (graph theory) , group of lie type , type (biology) , lie group , pure mathematics , lie theory , simple (philosophy) , group (periodic table) , classification of finite simple groups , combinatorics , classical group , algebraic number , simple group , sporadic group , representation of a lie group , algebra over a field , group theory , adjoint representation of a lie algebra , mathematical analysis , biology , ecology , philosophy , chemistry , lie conformal algebra , organic chemistry , epistemology
Let B be an irreducible spherical Moufang building of rank at least 2. Then the group G is called a group of Lie type B if it is generated by the root subgroups corresponding to the roots of some apartments of B. This notion includes: classical groups of finite rank, simple algebraic groups over arbitrary fields, the ‘mixed’ groups of Tits. General structure theorems and a general presentation type theorem for such Lie‐type groups, which in a way generalize well‐known theorems of Seitz and Curtis and Tits, are obtained. 1991 Mathematics Subject Classification : 20G15, 20E42.