Infinite Dimensional DeWitt Supergroups and their Bodies
2014 ◽
Vol 57
(2)
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pp. 283-288
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Keyword(s):
The Body
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AbstractFor 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 κ has the property that for each a ∊ κ ada has a zero spectrum. We also show that the exponential mapping from κ to K is surjective and that K is a quotient manifold of the Banach space κ via a lattice in κ.
Keyword(s):
2010 ◽
Vol 21
(11)
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pp. 1387-1399
Keyword(s):
2004 ◽
Vol 81
(1)
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pp. 93-120
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Keyword(s):
2009 ◽
Vol 146
(2)
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pp. 351-378
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2005 ◽
Vol 15
(03)
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pp. 793-801
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Keyword(s):