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Propriétés topologiques et combinatoires des échelles de numération

100%

Barat G., Downarowicz T., Iwanik A., Liardet P.

Colloquium Mathematicum

2000

tom 84/85

nr 2

285-306

Topological and combinatorial properties of dynamical systems called odometers and arising from number systems are investigated. First, a topological classification is obtained. Then a rooted tree describing the carries in the addition of 1 is introduced and extensively studied. It yields a description of points of discontinuity and a notion of low scale, which is helpful in producing examples of what the dynamics of an odometer can look like. Density of the orbits is also discussed.

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

58%

Burde D.

Open Mathematics

2006

tom 4

nr 3

323-357

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Open Mathematics

1 Barat G.

1 Burde D.

1 Downarowicz T.

1 Iwanik A.

1 Liardet P.

1 2006

1 2000

Wyniki wyszukiwania

Propriétés topologiques et combinatoires des échelles de numération

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