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On Finite-Dimensional Simple Novikov Algebras of Characteristic \( p \)

  • V. N. Zhelyabin,
  • A. S. Zakharov

摘要

Let $ N $ be a nonassociative finite-dimensional simple Novikovalgebra over an algebraically closed field $ F $ of characteristic $ p>0 $ . Thenthe right multiplication algebra  $ R $ is a differential simple algebrawith respect to some derivation  $ d $ . The algebra $ N $ is isomorphicto a Novikov algebra $ (R,d,R_{x}) $ for some operator of right multiplication by $ x $ and multiplicationis given by $ u\circ w=ud(w)+R_{x}uw $ .Moreover, the algebra $ R $ is a truncated polynomial algebra.