69 research outputs found
Contractions of Lie algebras and algebraic groups
Degenerations, contractions and deformations of various algebraic structures
play an important role in mathematics and physics. There are many different
definitions and special cases of these notions. We try to give a general
definition which unifies these notions and shows the connections among them.
Here we focus on contractions of Lie algebras and algebraic groups
Left-symmetric algebras, or pre-Lie algebras in geometry and physics
In this survey article we discuss the origin, theory and applications of
left-symmetric algebras (LSAs in short) in geometry in physics. Recently
Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics
(QFT and renormalization theory), where the name pre-Lie algebras is used quite
often. Already Cayley wrote about such algebras more than hundred years ago.
Indeed, LSAs arise in many different areas of mathematics and physics. We
attempt to give a survey of the fields where LSAs play an important role.
Furthermore we study the algebraic theory of LSAs such as structure theory,
radical theory, cohomology theory and the classification of simple LSAs. We
also discuss applications to faithful Lie algebra representations.Comment: 28 pages, 3 figure
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