Displaying similar documents to “Basic Representations of Affine Lie Algebras and Dual Resonance Models.”

On the combinatorics of Kac's asymmetry function

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....

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

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...

The construction of 3-Lie 2-algebras

Chunyue Wang, Qingcheng Zhang (2018)

Czechoslovak Mathematical Journal

Similarity:

We construct a 3-Lie 2-algebra from a 3-Leibniz algebra and a Rota-Baxter 3-Lie algebra. Moreover, we give some examples of 3-Leibniz algebras.

Family algebras.

Kirillov, A.A. (2000)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Similarity:

Drinfeld-Sokolov hierarchies on truncated current Lie algebras

Paolo Casati (2011)

Banach Center Publications

Similarity:

In this paper we construct on truncated current Lie algebras integrable hierarchies of partial differential equations, which generalize the Drinfeld-Sokolov hierarchies defined on Kac-Moody Lie algebras.

Affine Birman-Wenzl-Murakami algebras and tangles in the solid torus

Frederick M. Goodman, Holly Hauschild (2006)

Fundamenta Mathematicae

Similarity:

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.