Nichols Algebra And The Hecke Type Algebras

Let B(V, c) be a Nichols algebra , we introduced its Hecke-type Nichols sub-algebras . In the category of _H~HyD, where H is a group algebra, a necessary and sufficient condition is given for a braided vector space (V, c) to be a Hecke-type one. Let V be a finite dimension braided vector space, the necessary and sufficient condition is given for its braided vector subspace denoted U to be a Hecke-type subspace of V.Let A = T(V)/I_V be an algebra, we discuss the conditions when I_V is a coideal. The classification of quadratic Hopf algebras over a diagonal type braided vector space of 2-dimension and some Nichols algebras are provided.