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Lie monads and dualities

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arxiv 1302.6869 v2 pith:DDCC5NIU submitted 2013-02-27 math.RA math.CT

Isar Goyvaerts , Joost Vercruysse This is my paper · ORCID
classification math.RAmath.CT
keywords algebrasdualitiescoalgebrasmonadscomonadsdualitysenseyb-lie
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We study dualities between Lie algebras and Lie coalgebras, and their respective (co)representations. To allow a study of dualities in an infinite-dimensional setting, we introduce the notions of Lie monads and Lie comonads, as special cases of YB-Lie algebras and YB-Lie coalgebras in additive monoidal categories. We show that (strong) dualities between Lie algebras and Lie coalgebras are closely related to (iso)morphisms between associated Lie monads and Lie comonads. In the case of a duality between two Hopf algebras -in the sense of Takeuchi- we recover a duality between a Lie algebra and a Lie coalgebra -in the sense defined in this note- by computing the primitive and the indecomposables elements, respectively.

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  1. Towards interpolating categories for equivariant map algebras

    math.RT 2025-04 conditional novelty 7.0 of 10

    Categorical modules for (equivariant) map algebras are defined diagrammatically, and a candidate interpolating category Curr(OB) for current gl_n-modules is constructed, with its central fullness property left as a co...

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