A simplicial complex of Nichols algebras

Invariance of the barycentric subdivision of a simplicial complex

‎In this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎We also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.

On Isomorphism of Simplicial Complexes and Their Related Algebras

Incidence algebras of simplicial complexes

With any locally finite partially ordered set K its incidence algebra Ω(K) is associated. We shall consider algebras over fields with characteristic zero. In this case there is a correspondence K ↔ Ω(K) such that the poset K can be reconstructed from its incidence algebra up to an isomorphism — due to Stanley theorem. In the meantime, a monotone mapping between two posets in general induces no ...

invariance of the barycentric subdivision of a simplicial complex

‎in this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎we also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.

Lifting of Nichols Algebras of Type B 2 ∗

We compute liftings of the Nichols algebra of a Yetter-Drinfeld module of Cartan type B2 subject to the small restriction that the diagonal elements of the braiding matrix are primitive nth roots of 1 with odd n 6= 5. As well, we compute the liftings of a Nichols algebra of Cartan type A2 if the diagonal elements of the braiding matrix are cube roots of 1; this case was not completely covered i...