Universal measuring coalgebras and R - transformation algebras

Details Universal measuring coalgebras and R - transformation algebras Universal measuring coalgebras and R - transformation algebras

2009-12-07

arxiv.org/abs/0912.1204v1

Mathematics

Quantum Algebra

39

Scientific paper

Universal measuring coalgebras provide an enrichment of the category of algebras over the category of coalgebras. By considering the special case of the tensor algebra on a vector space V, the category of linear spaces itself becomes enriched over coalgebras, and the universal measuring coalgebra is the dual coalgebra of the tensor algebra T(V tensor V*). Given a braiding R on V the universal measuring coalgebra P_R(V) which preserves the grading is naturally dual to the Fadeev-Takhtadjhan-Reshitikin bialgebra A(R) and therefore provides a representation of the quantized universal enveloping algebra as an algebra of transformations. The action of P_R(V) descends to actions on quotients of the tensor algebra, whenever the kernel of the quotient map is preserved by the action of a generating subcoalgebra of P_R(V). This allows representations of quantized enveloping algebras as transformation groups of suitably quantized spaces.

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