Vertex algebras and algebraic curves
Edward Frenkel (1999-2000)
Séminaire Bourbaki
Similarity:
Edward Frenkel (1999-2000)
Séminaire Bourbaki
Similarity:
R. M. Green (2010)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
We use categories to recast the combinatorial theory of full heaps, which are certain labelled partially ordered sets that we introduced in previous work. This gives rise to a far simpler set of definitions, which we use to outline a combinatorial construction of the so-called loop algebras associated to affine untwisted Kac--Moody algebras. The finite convex subsets of full heaps are equipped with a statistic called parity, and this naturally gives rise to Kac's asymmetry function....
Harald Bjar, Olav Arnfinn Laudal (1990)
Compositio Mathematica
Similarity:
Hasiewicz, Zbigniew
Similarity:
Dietrich Burde (2006)
Open Mathematics
Similarity:
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...
M. Doubek, Martin Markl, Petr Zima (2007)
Archivum Mathematicum
Similarity:
First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation between deformations and solutions of the corresponding Maurer-Cartan equation. In Section we generalize the Maurer-Cartan equation to strongly homotopy Lie algebras and prove the homotopy invariance of the moduli space of solutions of this equation....