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Correction to “Infinite Dimensional DeWitt Supergroups and Their Bodies”
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- Journal:
- Canadian Mathematical Bulletin / Volume 58 / Issue 1 / 01 March 2015
- Published online by Cambridge University Press:
- 20 November 2018, pp. 69-70
- Print publication:
- 01 March 2015
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- Article
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Infinite Dimensional DeWitt Supergroups and their Bodies
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- Journal:
- Canadian Mathematical Bulletin / Volume 57 / Issue 2 / 14 June 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 283-288
- Print publication:
- 14 June 2014
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- Article
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- You have access
- Export citation
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For Dewitt super groups
$G$ modeled via an underlying finitely generated Grassmann algebra it is well known that when there exists a body group 
$BG$ compatible with the group operation on $G$, then, generically, the kernel 
$K$ of the body homomorphism is nilpotent. This is not true when the underlying Grassmann algebra is infinitely generated. We show that it is quasi-nilpotent in the sense that as a Banach Lie group its Lie algebra 
$\kappa$ has the property that for each 
$a\,\in \,\kappa ,\,\text{a}{{\text{d}}_{a}}$ has a zero spectrum. We also show that the exponential mapping from $\kappa$ to $K$ is surjective and that $K$ is a quotient manifold of the Banach space $\kappa$ via a lattice in $\kappa$.
