Affine varieties and Lie algebras of vector fields.
Gerd Müller, Herwig Hauser (1993)
Manuscripta mathematica
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Gerd Müller, Herwig Hauser (1993)
Manuscripta mathematica
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V.G. Kac, I.B. Frenkel (1980/81)
Inventiones mathematicae
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Dietrich Burde (2006)
Open Mathematics
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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...
Leitenberger, Frank (1994)
Journal of Lie Theory
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Dietrich Burde (2007)
Archivum Mathematicum
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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.
Karl Heinrich Hofmann, W.A.F. Ruppert (1994)
Mathematische Annalen
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Ben Yakoub, L., Louly, A. (2009)
Beiträge zur Algebra und Geometrie
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Kailash C. Misra (1990)
Mathematische Annalen
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Georgia Benkart, Thomas Gregory (1989)
Mathematische Annalen
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Galitski, L.Yu., Timashev, D.A. (1999)
Journal of Lie Theory
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Ciobanu, Camelia (2007)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Frederick M. Goodman, Holly Hauschild (2006)
Fundamenta Mathematicae
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The affine Birman-Wenzl-Murakami algebras can be defined algebraically, via generators and relations, or geometrically as algebras of tangles in the solid torus, modulo Kauffman skein relations. We prove that the two versions are isomorphic, and we show that these algebras are free over any ground ring, with a basis similar to a well known basis of the affine Hecke algebra.