## Homology, Homotopy and Applications

- Homology Homotopy Appl.
- Volume 4, Number 2 (2002), 165-190.

### Trees, free right-symmetric algebras, free Novikov algebras and identities

Askar Dzhumadiľdaev and Clas Löfwall

#### Abstract

An algebra with the identity $x\circ (y\circ z-z\circ y)= (x\circ y)\circ z-(x\circ z)\circ y$ is called right-symmetric. A right-symmetric algebra with the identity $x\circ(y\circ z)= y\circ(x\circ z)$ is called Novikov. We describe bases of free right-symmetric algebras and free Novikov algebras and give realizations of them in terms of trees. The free Lie algebra is obtained as a Lie subalgebra of the free right-symmetric algebra. We use our methods to study identities of Witt algebras.

#### Article information

**Source**

Homology Homotopy Appl., Volume 4, Number 2 (2002), 165-190.

**Dates**

First available in Project Euclid: 13 February 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.hha/1139852461

**Mathematical Reviews number (MathSciNet)**

MR1918188

**Zentralblatt MATH identifier**

1029.17001

**Subjects**

Primary: 17A30: Algebras satisfying other identities

#### Citation

Dzhumadiľdaev, Askar; Löfwall, Clas. Trees, free right-symmetric algebras, free Novikov algebras and identities. Homology Homotopy Appl. 4 (2002), no. 2, 165--190. https://projecteuclid.org/euclid.hha/1139852461