ON THE LIE ALGEBRA OF HOLOMORPHIC AFFINE VECTOR FIELDS OF HOLOMORPHIC LINEAR CONNECTIONS WITH SYMMETRIC RICCI TENSOR FIELD

Abstract: 

The author of the article studies the Lie Algebra of holomorphic affine vector fields of holomorphic linear connections defined on smooth manifolds over Algebras. He establishes maximal real dimension of the Lie Algebras of holomorphic affine vector fields, and constructs the examples that prove that the maxi-mum dimension of the Lie Algebras of holomorphic affine vector fields may be obtained.

Key words: 

Unital Algebra, Commutative Algebra, Associative Algebra, Smooth Manifold, Holomor-phic Linear Connection, Affine Holomorphic Vector Field, Lie Algebra of Holomorphic Affine Vector Fields.

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