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

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.

Added an article, [4], and two remarks, Remarks 3.8 and 7.3

References in corpus (3)

• The Minkowski and conformal superspaces
• Hopf algebraic techniques applied to super algebraic groups
• Geometric construction of quotients $G/H$ in supersymmetry

Cited by in corpus (1)

• Geometric construction of quotients $G/H$ in supersymmetry