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On simple Novikov algebras and their irreducible modules. (English) Zbl 0863.17003

An algebra A is called Novikov if (x,y,z)=(y,x,z) and (xy)z=(xz)y for all x,y,zA. The author gives a complete classification of finite-dimensional simple Novikov algebras and their irreducible modules over an algebraically closed field F with prime characteristic p>2. (In particular, if A is a finite-dimensional simple Novikov algebra over F, then for some positive integer n there is a basis {y -1 ,y 0 ,,y p n -2 } for A such that

y i y j =i+j+1 jy i+j +δ i,-1 δ j,-1 ay p n -2 +δ i,-1 δ j,0 by p n -2 ,

where a, bF are constants. (Here y k =0 if k{-1,0,,p n -2}·)) The author also introduces what he calls “Novikov-Poisson algebras” and their tensor theory. All of this builds on the results in a number of articles by J. M. Osborn.


MSC:
17A30Nonassociative algebras satisfying other identities