Remarks on quadratic left Bol algebras

Abstract: In this paper the notion of a quadratic (left) Bol algebra is discussed. Several examples of quadratic Bol algebras are given and it is observed that the only two-dimensional quadratic real Bol algebras are quadratic Lie triple systems. Dual representations of Bol algebras are investigated with a particular emphasis on coadjoint representations for quadratic Bol algebras. The notion of T*-extension of a quadratic Bol algebra is introduced.