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 Universal measuring coalgebras and R - transformation algebras


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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 TV tensor V*. Given a braiding R on V the universal measuring coalgebra P RV which preserves the grading is naturally dual to the Fadeev-Takhtadjhan-Reshitikin bialgebra AR and therefore provides a representation of the quantized universal enveloping algebra as an algebra of transformations. The action of P RV 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 RV. This allows representations of quantized enveloping algebras as transformation groups of suitably quantized spaces.



Autor: Marjorie Batchelor; Jordan Thomas

Fuente: https://archive.org/







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