gammaendomorphisms

Gamma-endomorphisms are a type of map, specifically an endomorphism, between a non-associative algebra and itself. A non-associative algebra is a generalization of a vector space, describing not only the basic operations of vector space, but also multiplication. These operations need not be associative, that is, there is not always an equal left and right simplification when changing multiplication between two vector values and one other.

A gamma-endomorphism is a homomorphism between gamma-algebras. The homomorphism condition requires that the gamma endomorphism preserves the multiplication given in the gamma-algebra. Gamma-endomorphisms are part of a broader category of maps, which include gamma-derivations and gamma-anticommutators.

In contrast to endomorphisms in vector spaces, gamma-endomorphisms have to take into consideration the non-associative nature of the operations in the algebra. They act as the counterpart to brute derivatives when sweeping beneath the intricacies of many types of involutive orthomorphisms. They are a fundamental tool in abstract algebra.

Gamma-endomorphisms are also used in the study of gamma-modules, specifically to describe a mapping of a module to itself under the action of a gamma algebra.

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