ABSTRACT
This chapter examines commutative, finite dimensional algebras over an infinite field K, char K ≠ 2. A baric algebra (A, w) is a K-algebra having a nonzero homomorphism of algebras w : A → K (weight homomorphism). The chapter lists some known properties of second order Bernstein algebras. It examines the algebra of derivations Der(A) in a second order Bernstein algebra A. A bound for dimKDer(A) is found. This bound is reached in the case of a second order Bernstein algebra. Some particular cases of power-associative second order Bernstein algebras with Der(A) ≠ 0 are studied. The chapter proves that in a Jordan second order Bernstein algebra Der(A) ≠ 0, and gives a description of the set of inner derivations of A.
