Journal of Lie Theory

no. 1
The Left-Regular Representation of a Super Lie Group
Journal of Lie Theory, Volume 29 (2019) no. 1, pp. 1-78
With the usual definition of a super Hilbert space and a super unitary representation, it is easy to show that there are lots of super Lie groups for which the left-regular representation is not super unitary. I will show that weakening the definition of a super Hilbert space (by allowing the super scalar product to be non-homogeneous, not just even) will allow the left-regular representation of all (connected) super Lie groups to be super unitary (with an adapted definition). Along the way I will introduce a (super) metric on a supermanifold that will allow me to define super and non-super scalar products on function spaces.
DOI: 10.5802/jolt.1046
Classification: 58A50, 22E99, 57S20
Keywords: Super manifolds, super Lie groups, regular representation, super unitary representation 
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     author = {G. M. Tuynman},
     title = {The {Left-Regular} {Representation} of a {Super} {Lie} {Group}},
     journal = {Journal of Lie Theory},
     pages = {1--78},
     year = {2019},
     volume = {29},
     number = {1},
     doi = {10.5802/jolt.1046},
     zbl = {1418.58003},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1046/}
}
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G. M. Tuynman. The Left-Regular Representation of a Super Lie Group. Journal of Lie Theory, Volume 29 (2019) no. 1, pp. 1-78. doi: 10.5802/jolt.1046

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