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arXiv · 2003.04588

The Drinfeld-Kohno theorem for the superalgebra $gl(1|1)$

A. Babichenko
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Abstract

We revisit the derivation of Knizhnik-Zamolodchikov equations in the case of nonsemisimple categories of modules of a superalgebra in the case of the generic affne level and representations parameters. A proof of existence of asymptotic solutions and their properties for the superalgebra $gl(1|1)$ gives a basis for the proof of existence associator which satisfy braided tensor categories requirements. Braided tensor category structure of $U_h(gl(1|1))$ quantum algebra calculated, and the tensor product ring is shown to be isomorphic to $gl(1|1)$ ring, for the same generic relations between the level and parameters of modules. We review the proof of Drinfeld-Kohno theorem for non-semisimple category of modules suggested by Geer and show that it remains valid for the superalgebra $gl(1|1)$. Examples of logarithmic solutions of KZ equations are also presented.

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BibTeXRIS

A. Babichenko. 2020-03-10. The Drinfeld-Kohno theorem for the superalgebra $gl(1|1)$. https://doi.org/10.1007/s11005-021-01412-2

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