Left-symmetric algebras, or pre-Lie algebras in geometry and physics

Dietrich Burde

Open Mathematics (2006)

  • Volume: 4, Issue: 3, page 323-357
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Dietrich Burde. "Left-symmetric algebras, or pre-Lie algebras in geometry and physics." Open Mathematics 4.3 (2006): 323-357. <http://eudml.org/doc/269024>.

@article{DietrichBurde2006,
abstract = {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.},
author = {Dietrich Burde},
journal = {Open Mathematics},
keywords = {17-02; 22-02 53-02},
language = {eng},
number = {3},
pages = {323-357},
title = {Left-symmetric algebras, or pre-Lie algebras in geometry and physics},
url = {http://eudml.org/doc/269024},
volume = {4},
year = {2006},
}

TY - JOUR
AU - Dietrich Burde
TI - Left-symmetric algebras, or pre-Lie algebras in geometry and physics
JO - Open Mathematics
PY - 2006
VL - 4
IS - 3
SP - 323
EP - 357
AB - 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.
LA - eng
KW - 17-02; 22-02 53-02
UR - http://eudml.org/doc/269024
ER -

References

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