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Lie Algebroids and Lie Pseudoalgebras
Author(s) -
Mackenzie Kirill C. H.
Publication year - 1995
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/27.2.97
Subject(s) - mathematics , adjoint representation , graded lie algebra , lie theory , algebra over a field , fundamental representation , pure mathematics , adjoint representation of a lie algebra , differential geometry , lie algebra , simple lie group , variety (cybernetics) , representation of a lie group , representation theory , lie conformal algebra , weight , statistics
Lie algebroids and Lie pseudoalgebras arise from a wide variety of constructions in differential geometry; they have been introduced repeatedly into the geometry, physics and algebra literatures since the 1950s, under some 14 different terminologies. The first main part (Sections 2–5) of this survey describes the four principal classes of examples, emphazising that each arises by means of a generalization of the Lie theory of Lie groups and Lie algebras; this part is addressed primarily to those interested in differential geometry. The second part (Sections 7–8), addressed equally to algebraists, describes various algebraic constructions currently known for Lie algebroids and Lie pseudoalgebras, and their geometric significance.