A Study On Left - Symmetric Algebra Based On DNA Embedding

In this paper, we mainly consider the generalizations of left-symmetric al-gebras (LSAs in short) in Biological gene recombination. Indeed., LSAs play an important role in many areas. D. Brude[] discussed the theory and applications of LSAs in Geometry and Physics. Connes. Kreimer and Kontsevich introduced the application of LSAs in mathematical physics. The theory of LSAs has a close bond with the Quantum Field Theory. In all, the theory of LSAs has good prospects in many fields.We mainly propose a modified left symmetric algebraic structure in Biolog-ical gene recombination, which generalize the left symmetric algebra constructed by the simplified insertions. First, we introduce the left symmetric DNA simpli-fied insertion algebras. Considering the subspaces of the algebras, we illustrate the conditions satisfying the left symmetric identities by graphs. Further, We construct new DNA insertion operation because of the reality of nature and then we construct the new modified left-symmetric algebra due to this new operation. Finally, we study the structure of the new algebra.