Cocommutative Hopf algebras with antipode.

After reviewing the definition of the restricted quantum group U q sℓ(2), we give our quasi-Hopf algebra modification U (Φ) q sℓ(2), and we show that it is indeed a factorisable

The map κ from signed per- mutations to Cambrian trees is known to encode combinatorial and geometric properties of the Cambrian structures: the Cambrian lattice is the quotient of

The abelian core of the category of cocommutative Hopf algebras over a field of characteristic zero is the category of commutative and cocommutative Hopf algebras.. Roughly speaking

This new algebra is a true Hopf deformation which reduces to LDIAG for some parameter values and to the algebra of Matrix Quasi-Symmetric Functions ( MQSym ) for others, and

A further non-commutative Hopf algebra of TAGs can be defined when considering only graphs of a given quantum field theoretical model and defin- ing the coproduct as the appropriate

The classes of (labelled) diagrams up to this equivalence (permutations of white - or black - spots among themselves) are naturally represented by unlabelled diagrams and will

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A key example of this is the Hopf algebra of graphs G as given in [16], where the authors derive the antipode formula and use it to obtain the celebrated Stanley’s (−1)-color