AN ANALOGUE OF KEGEL'S THEOREM FOR QUASI-ASSOCIATIVE ALGEBRAS

Abstract

Let H be a quasi-Hopf algehra and A a quasi-associative algebra in ^H _H YD. Let X and Y be subalgebras of A in ^H _H YD that are quasi H-commutative and are such that m = m^x + m^y, where m, m^x = m|_x and m^y = m|_y denotes the multiplication of A, X und Y respectively. If the braiding C_{A, A} is Symmetric on A, then we obtain the morphism identity: m_A((m − mC_x,y) ⊗ (m − mC_x,y)) = 0. As an application of our theory, we get an analogue of the classical Kegel's theorem for quasi-associative algebra in Corollary 4.13, generalizing the one in Wang (2002).

Key Words:

• Braided monoidal category
• Kegel's theorem
• Quasi braided Lie algebra
• Quasi-Hopf algebra