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arXiv · 1706.02839

Hopf-algebraic techniques applied to super Lie groups over a complete field

Mitsukazu Hoshi·Akira Masuoka·Yuta Takahashi
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Abstract

We show basic results on super-manifolds and super Lie groups over a complete field of characteristic $\ne 2$, extensively using Hopf-algebraic techniques. The main results are two theorems. The first main theorem shows a category equivalence between super Lie groups and Harish-Chandra pairs, which is applied especially to construct the Hopf super-algebra of all analytic representative functions on a super Lie group. The second constructs homogeneous super-manifolds by a new Hopf-algebraic method, showing their remarkable property.

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Mitsukazu Hoshi, Akira Masuoka, Yuta Takahashi. 2017-06-09. Hopf-algebraic techniques applied to super Lie groups over a complete field. https://doi.org/10.1016/j.jalgebra.2020.06.019

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