The Left-Regular Representation of a Super ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
The Left-Regular Representation of a Super Lie Group
Author(s) :
Journal title :
Journal of Lie Theory
Pages :
001-078
Publisher :
Heldermann Verlag
Publication date :
2019
ISSN :
0949-5932
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Popular science :
Non
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