Mihai D. Staic

PURE-BRAIDED HOPF ALGEBRAS AND KNOT INVARIANTS

In this paper we construct representations for the pure braid group using Hopf algebra techniques. From this representations we obtain invariants for knots.

Remarks on 2–dimensional HQFTs

We introduce and study algebraic structures underlying 2-dimen- sional Homotopy Quantum Field Theories (HQFTs) with arbitrary target spaces. These algebraic structures are formalized in the notion of a twisted Frobenius algebra. Our work generalizes results of Brightwell, Turner, and the second author on 2-dimensional HQFTs with simply-connected or aspherical targets.

MORE EXAMPLES OF PSEUDOSYMMETRIC BRAIDED CATEGORIES

We study some examples of braided categories and quasitriangular Hopf algebras and decide which of them is pseudosymmetric, respectively pseudotriangular. We show also that there exists a universal pseudosymmetric braided category.

Automorphisms of the k-algebra k[X1,…,Xm]

For a field

Generalized (anti) Yetter-Drinfeld modules as components of a braided T-category

k

Pseudosymmetric braidings, twines and twisted algebras

of characteristic

On some classes of lazy cocycles and categorical structures

0

From 3-algebras to Δ-groups and symmetric cohomology

, we present an algorithm for deciding if a morphism

A quotient of the braid group related to pseudosymmetric braided categories

\phi:k[X_1,...,X_m]\to k[X_1,...,X_m]

Symmetric cohomology of groups in low dimension

has an inverse. The algorithm also shows how to find the inverse when it exists.