The description of dendriform algebra structures on two-dimensional complex space (Q2889953)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The description of dendriform algebra structures on two-dimensional complex space |
scientific article; zbMATH DE number 6044079
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The description of dendriform algebra structures on two-dimensional complex space |
scientific article; zbMATH DE number 6044079 |
Statements
8 June 2012
0 references
dendriform algebras
0 references
two-dimensional algebras
0 references
isomorphism classes
0 references
nilpotency
0 references
dialgebras
0 references
Leibniz algebras
0 references
The description of dendriform algebra structures on two-dimensional complex space (English)
0 references
A dendriform algebra is an algebra with two multiplications \(\prec\) and \(\succ\) satisfying three axioms which guarantee that the multiplication \(x\ast y=x\prec y+x\succ y\) is associative. In the paper under review the authors classify all two-dimensional complex dendriform algebras. There are twelve isomorphism classes. One of the classes depends on one parameter and each of the other eleven classes consists of a single algebra. In order to obtain their classification the authors establish some properties of nilpotent dendriform algebras which are of independent interest.
0 references
