On a construction connecting Lie algebras with general algebras. (English) Zbl 0678.17016

Michor, P.; Ruppert, W.; Wegenkittl, K.

Proc. Winter Sch. Geom. Phys., Srní/Czech. 1988, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 21, 265-274 (1989).

[For the entire collection see Zbl 0672.00006.]
The paper introduces a general construction which associates an algebra A(\({\mathfrak L},b)\) with every pair (\({\mathfrak L},b)\), where \({\mathfrak L}\) is a Lie algebra and b is an invariant symmetric bilinear form on \({\mathfrak L}\). This construction leads to a unifying view of several well-known (associative and nonassociative) algebras.
The paper characterizes the pairs (\({\mathfrak L},b)\) which generate associative algebras A(\({\mathfrak L},b)\) and the algebras A which can be represented in the form A(\({\mathfrak L},b)\).

Reviewer: M.Modugno

MSC:

17B99	Lie algebras and Lie superalgebras
17A60	Structure theory for nonassociative algebras

Keywords:

general construction; Lie algebra; invariant symmetric bilinear form; associative algebras

Citations:

Zbl 0672.00006