A new class of non-associative algebras with genetic realizations

Abstract

In this paper we introduce a new class of non associative algebras and found the direction of its applications in quantum mechanics. We show that a noncommutative and non-associative algebra form a baric algebra.We introduce generalized Jordan algebra which is non-associative and non-commutative but satisfies the Jordan identity. Moreover by defining a new operation on left almost algebra, it becomes commutative, associative and satisfies Jordan identity.